Part BCSIR NET June 2024rank-nullity-inequality-direction

Rank nullity inequality direction

Let $A : R^{m} \to R^{n}$ be a non-zero linear transformation. Which of the following statements is true?

A.If A is one-to-one but not onto, then m > n
B.If A is onto but not one-to-one, then m < n
C.If A is bijective, then m = n✓
D.If A is one-to-one, then m = n

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests converse assumed.

See pricing

50 are analysed free — try those first.

The trap it tests

Converse assumed

The theorem runs one way. You used it in the other.

Drill statements like this

Rank nullity inequality direction

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