Lot A a1 a2 a3 a4 be a 4 times 4 matrix and suppose that a1

Lot A = (a_1, a_2, a_3, a_4)) be a 4 times 4 matrix and suppose that a_1 - 3a_2 = 2a_3 - a_4. Is the system Ax = 0 consistent arid if so, how many solutions will it have? Is A nonsingular?

Solution

A is a 4x4 square matrix.

Since given that a1-3a2 = 2a3-a4

we see that the determinant will become identical with two columns

Hence |A| =0

So A is not non singular and A is singular.

Ax=0 will be consistent as right side is 0

But no unique solution is possible infinite dependent solutions are possible.