Consider the following four matrices from the vector space M2×3 of all 2 × 3 matrices:

A1 = 2 1 −3 2 −2 4 , A2 = 1 2 −12 −2 3 2 , A3 = 2 −2 0 −1 5 4 , A4 = 0 2 −4 1 −3 0 .

(a) Let vi denote the coordinate vector [Ai ]E relative to the basis E = 1 0 0 0 0 0 , 0 1 0 0 0 0 , 0 0 1 0 0 0 , 0 0 0 1 0 0 , 0 0 0 0 1 0 , 0 0 0 0 0 1 . Enter the coordinate vectors for A1, A2, A3, A4 into MATLAB.

(b) Use MATLAB to show that the coordinate vectors v1, v2, v3, v4 are linearly dependent.

(c) ? Express one of the matrices Ai as a linear combination of the other three. (Hint: first do the same for the coordinate vectors.)