# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 25 results; page 1/1. ## Question 17101: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0026`; number: 17101 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0026/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0026/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0026.json) ## Question 17102: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0027`; number: 17102 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0027/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0027/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0027.json) ## Question 17103: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0028`; number: 17103 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0028/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0028/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0028.json) ## Question 17104: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0029`; number: 17104 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0029/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0029/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0029.json) ## Question 17105: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0030`; number: 17105 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0030/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0030/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0030.json) ## Question 17106: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0031`; number: 17106 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0031/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0031/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0031.json) ## Question 17107: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0032`; number: 17107 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0032/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0032/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0032.json) ## Question 17108: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0033`; number: 17108 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0033/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0033/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0033.json) ## Question 17109: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0034`; number: 17109 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0034/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0034/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0034.json) ## Question 17110: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0035`; number: 17110 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0035/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0035/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0035.json) ## Question 17111: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0036`; number: 17111 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0036/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0036/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0036.json) ## Question 17112: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0037`; number: 17112 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0037/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0037/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0037.json) ## Question 17113: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0038`; number: 17113 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0038/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0038/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0038.json) ## Question 17114: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0039`; number: 17114 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0039/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0039/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0039.json) ## Question 17115: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0040`; number: 17115 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0040/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0040/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0040.json) ## Question 17116: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0041`; number: 17116 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0041/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0041/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0041.json) ## Question 17117: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0042`; number: 17117 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0042/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0042/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0042.json) ## Question 17118: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0043`; number: 17118 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0043/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0043/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0043.json) ## Question 17119: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0044`; number: 17119 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0044/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0044/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0044.json) ## Question 17120: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0045`; number: 17120 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0045/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0045/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0045.json) ## Question 17121: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0046`; number: 17121 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0046/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0046/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0046.json) ## Question 17122: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0047`; number: 17122 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0047/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0047/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0047.json) ## Question 17123: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0048`; number: 17123 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0048/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0048/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0048.json) ## Question 17124: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0049`; number: 17124 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0049/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0049/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0049.json) ## Question 17125: Give a Basis of the Entire Real Kernel, Not a Finite Search Result - ID: `q-20261014-advance-20261102-r02-linear-map-kernel-0050`; number: 17125 - Processing: second_context_reviewed - MKO: [mko-linear-map-kernel](/en/mko/mko-linear-map-kernel/) - Family: [qf-mod33-kernel-basis](/en/explore/?family=qf-mod33-kernel-basis) - Batch: [batch-20261014-advance-20261102-r02-linear-map-kernel-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r02-linear-map-kernel-foundations) - [Derivation](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0050/) / [Markdown](/en/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0050/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r02-linear-map-kernel-0050.json)