4. Find the null space and column space of the matrices 0 1 1 -2 1 1 0 1 22-4 0 -1 0 1 -3 A = 1 2 3 -1 3 2 " B = -1 and C-(²2) 글). c = C= 1 0

Show that if A is square matrix that satisfies the equation 2 A² - A - I = O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- ✓. It follows that ---Select--- ✓. Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.

Let A, B, C be 2×2 matrices where B = - /2 A, det A =2 and 8. Then det (8 A ³ (B -1)T c-2) = der (8 A3 (B-1)Tс-3) 3D det C= – O -2 4 O -4 2.