# Determine if each of the following statements is true or false

Transcribed Image Text: Problem 1.

Determine if each of the following statements is true or false.

Supporting work is not required.

Let T : R’ → R3 be a surjective linear transformation. Let A be the matrix

corresponding to T. Then rankA = 3.

True

False

There exists a 4 × 5 matrix A satisfying rankA = nullity A.

True

False

Let A be a matrix, and B,C be two (arbitrary) echelon forms of A. Then

det B = det C.

True

False

| Let A be a n x n matrix such that A2021

A. If v is an eigenvector of A,

then v is an eigenvector of A2021.

True

False

Let A be a n x n matrix. Suppose that A has n distinct eigenvalues, then A

is diagonalizable.

True

False

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