Determine whether the following set of real matrices, S = {A1, A2, A3}, where: Αν = − 2 3 ] 4 = [ 2 ] 4 = 2 −1 ] , A3 A2 is linearly independent or linearly dependent. If it is linearly dependent, find a non-trivial linear combination of the matrices A1, A2, A3 which is equal to the zero matrix.

Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.

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

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

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.

Let A and B be square matrices of order 4 such that |A|=5 and |B|=3.Find a |A2|, b |B2|, c |A3|, and d |B4|

Show that the matrix below does not have an LU factorization. A=0110