-4 8 9 0 2 1. For the matrices A = B = 1 3 0 1 and C = 48 0 -1 5 3 (if possible) (a) Ax B (b) A +3C (c) B x C (d) AT, BT, and CT -1 (2) -1 2 find

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?

Solve for x and y in the matrix equation 2AB=I, given A=[1123] and B=[x2y5].

15. Reverse the elementary row operations used in Example 2.9 to show that we can convert

Let X1,X2,X3 and b be the column matrices below. X1=[101], X2=[110], X3=[011] and b=[123] Find constants a, b, c and c such that aX1+bX2+cX3=b

Solve for x,y,z and w in the matrix equation wxyx=-432-1+2ywzx.

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?