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Question

Let A 3 be the matrices A e M3 (R), B e M3,4 (R) and C e M3,5 (Z5)

(2 3 -11

A: 123,

3 4 -4/

/1 0 1 -1

B:= 0 2 0 1

-1 1 0 0,

(1 3 1 1 1

C:= 2 1 1 1 2

4 2 1 0 1/

(a) Determine A-1 using the Gauss-Jordan algorithm (please no ready-made solution-

use the formula for 3 x 3 matrices and/or the determinant).

(b) Let X be € M3.4(R). Solve AX= B.

(c) Determine the dimension and a basis of ker(C).

(3 + 1 + 3 Points)

Fig: 1