1. If the order of the matrix is mxn, then how many elements will there be in the matrix? a. mn b. m'n C. mn

Describe the possible echelon forms of the matrices below using 0, 1 for the pivot and * for all other entries. a. A is a 2x2 matrix with linearly independent columns. b. A is a 4x3 matrix, A= a, a, az such that {a,,a,} is linearly independent and a, is not in span{a,,a,} С. How many pivot columns must a 6x4 matrix have if its columns are independent? Why?

I believe A is correct, but I am not sure about w. It needs to be written as a fraction. Thanks!

Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: a. If you exchange two rows of A to produce matrix B, then det(A) = -det(B). b. det A" = det A c. |AC| = |A||C| d. Using property c above, show that det Ak = (det A)k for some natural number k. Show that detrA = r² det A, for some scalar r. е.