3. Let A be an invertible matrix such that A-¹ = NOT 2 0 1 2 01 1 1 Solve the system (2A2)x= b, where b = 3 0 473

-1 Suppose A, B, C, X are invertible n x n matrices. Solve the matrix equation C(B1X) = (B-²C-1) B² (A-³C)¯' for X, simplifying as much as possible (but no further!).

-1 1 -3 2 2 -3 -2] M³+c₁M² + c₂M + c3I3 = 0, where I3 is the identity 3 x 3 matrix. Let M C1 || C2 = C3 = -3] 3. Find C₁, C₂, and c3 such that 1

Consider the following linear equations: -2x + 4y + 10z = -5 -2x + (22-k)y+9z = -3 -2x + 4y+(12-k)z =k+9 a) Suppose the above equation is expressed as Ax = b with x = equations in one matrix form as (Alb)= -2 -2 -2 4 -2 10 4 X3 10 -5 b) Use row operations on (Alb) by substracting row 1 from row 2 and row 3 respectively. Fill in the missing entries: Express the coefficients of the -5 Submit part 3 marks Unanswered

(a) A is a 3 x 3 matrix and 2(A + I) = I. Enter det (A + I). (b) A is a 2 x 2 matrix and 2 A + 5 I = 0. Enter det (4+ I). (c) A is a 4 x 4 matrix and 42 - 4 A -21 1= 0. If det (A-21) > 0, enter det (4-21).

Use Cramer's Rule to solve the 3 x 3 matrix A- 3B + 7Z = 13 A +B+Z = 1 A – 2B + 3Z = 4