A 1 let the following system of linear equations be given over R:

X1 + X2

2x1 +4x2

4x1 + 2x2

21 + X2

+ AX5

+ X4 X5

+ 3x4 + X5

(i) no solution,

(ii) exactly one solution,

= 1

= 1

= 1

= 1

Bx3

(a) Let B = = 1. Write the LGS in matrix form Ax = b and calculate the The

rank of A and the rank of the extended coefficient matrix (A, b) for a = 0, and

a = 1.

(b) Determine a, B, y € R in each case so that the LGS

(iii) has an infinite number of solutions.

(4.5+ 1.5 Points)