# OCME · 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 17676: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0026`; number: 17676
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0026/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0026/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0026.json)

## Question 17677: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0027`; number: 17677
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0027/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0027/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0027.json)

## Question 17678: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0028`; number: 17678
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0028/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0028/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0028.json)

## Question 17679: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0029`; number: 17679
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0029/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0029/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0029.json)

## Question 17680: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0030`; number: 17680
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0030/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0030/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0030.json)

## Question 17681: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0031`; number: 17681
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0031/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0031/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0031.json)

## Question 17682: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0032`; number: 17682
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0032/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0032/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0032.json)

## Question 17683: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0033`; number: 17683
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0033/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0033/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0033.json)

## Question 17684: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0034`; number: 17684
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0034/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0034/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0034.json)

## Question 17685: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0035`; number: 17685
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0035/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0035/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0035.json)

## Question 17686: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0036`; number: 17686
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0036/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0036/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0036.json)

## Question 17687: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0037`; number: 17687
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0037/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0037/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0037.json)

## Question 17688: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0038`; number: 17688
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0038/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0038/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0038.json)

## Question 17689: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0039`; number: 17689
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0039/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0039/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0039.json)

## Question 17690: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0040`; number: 17690
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0040/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0040/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0040.json)

## Question 17691: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0041`; number: 17691
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0041/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0041/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0041.json)

## Question 17692: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0042`; number: 17692
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0042/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0042/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0042.json)

## Question 17693: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0043`; number: 17693
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0043/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0043/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0043.json)

## Question 17694: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0044`; number: 17694
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0044/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0044/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0044.json)

## Question 17695: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0045`; number: 17695
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0045/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0045/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0045.json)

## Question 17696: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0046`; number: 17696
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0046/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0046/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0046.json)

## Question 17697: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0047`; number: 17697
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0047/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0047/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0047.json)

## Question 17698: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0048`; number: 17698
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0048/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0048/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0048.json)

## Question 17699: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0049`; number: 17699
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0049/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0049/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0049.json)

## Question 17700: A Nonzero Minor Supplies a Lower Bound, Not Automatically Exact Rank

- ID: `q-20261014-advance-20261103-r01-matrix-rank-0050`; number: 17700
- Processing: second_context_reviewed
- MKO: [mko-matrix-rank](/en/mko/mko-matrix-rank/)
- Family: [qf-mod34-rank-minor-lower-bound](/en/explore/?family=qf-mod34-rank-minor-lower-bound)
- Batch: [batch-20261014-advance-20261103-r01-matrix-rank-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r01-matrix-rank-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0050/) / [Markdown](/en/questions/q-20261014-advance-20261103-r01-matrix-rank-0050/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r01-matrix-rank-0050.json)