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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