Find a sequence of elementary matrices that can be used to write the matrix in row-echelon form. 1 -2 -1 6 -3 -7 14 9. 1 0 0 1 0 0 1/2 1 0 0 0 1 0 -7 0 1 1 0 0 0 1/3 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 O 1/3 0 1/2

Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.

Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be used to create a leading 1 at the top of the first column. Which do you prefer and why?

The two matrices A and B are row-equivalent. A=[240171112119121213516481162] B=[120032001053000117000000] (a) Find the rank of A. (b) Find the basis for the row space of A. (c) Find the basis for the column space of A. (d) Find the basis for the null space of A. (e) Is the last column of A in the span of the first three columns of A? (f) Are the first three column s of A linearly independent? (g) Is the last column of A in the span of columns 1, 3, and 4? (h) Are the columns 1, 3, and 4 linearly dependent?