MathAlgebraLinear algebraSystems of linear equations

Matrix rank

Can it be?

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Alice, a math teacher, gave her students a $10\times5$ matrix and asked them to calculate its rank. The teacher hadn't computed the rank previously, nevertheless, when the first student to solve the problem gave her the answer: $\text{rank} = 7$ , she immediately said, that it is incorrect. Why could that happen?

Select one option from the list

The rank of a matrix

m\times n

is not greater than

\min(m, n)

The rank of a matrix can't be an odd number

The rank of a matrix is always equal to

\min(m, n)

The teacher was mistaken, the answer could have been correct

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