Taking Matrices Apart Let A be an n × n matrix whose jth column is the column vector (n ×...

Taking Matrices Apart Let A be an n × n matrix whose jth column is the column vector (n × 1 matrix) Aj; we can write this as [A1 | A2 | ⋯ | An] (an example of a partitioned matrix). Let be the column vector [x1 x2 ⋯ xn]T.

(a)

(b) Show that in general the product of a matrix and a vector can be expressed as a linear combination of the columns of the matrix; that is, show that (8) is a true statement independent of the particular matrices in part (a).