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Family 6
Rank–nullity: augmented & geometry
These 3 topics share one solution. Spot the family, apply the method — same trick, different story.
How to spot this family
- Rank, augmented matrix & solution set："A is m×n with rank r ... possible values for the rank of B=(A|b)" · (b) 问解集的几何描述
- Nullity, augmented matrix & solvable b："A is m×n with nullity k ... possible values for the nullity of B" · (b) 使 Ax=b 有解的 b 组成什么
- Rank–nullity theorem contradiction："your friend claims to have created an m×n matrix with rank r and nullity k" · 选一个「为什么不可能」的理由
Topics in this family
Topic 9New
Rank, augmented matrix & solution set
14
Topic 10New
Nullity, augmented matrix & solvable b
10
Topic 11New
Rank–nullity theorem contradiction
9
Related knowledge points
The concepts behind this family's method — brush up first if unsure.