Linear Algebra Determinants

Question

Let A = [(a-1) -2 2 -1 (a-3) 1 -1 -4 (a+2)] 3x3 matrix

(a) For what values of a will the homogenous system Ax = 0 have infinitely many solutions ?

(b) For each values of a found in (a) write down the general solution.

i have done (a) and found out the values of a = -1, 1 and 2, am I correct?

Answer 1

DetA = 0; a³ -2a² - a + 2 = 0; (a - 2)(a - 1)(a + 1) = 0; a = 2 or a = 1 or a = - 1