Question

6. Given matrices A=[[3,2,4],[3,1,3],[1,4,1]] and B=[[4,2,2],[1,5,2],[2,1,4]]. (a)(i) Find the determinant of A. (ii) Find the determinant of B. (b) Find the inverse of A. (12 marks)

Accepted Answer

(a)(i) |A| = 3(1x1-3x4) - 2(3x1-3x1) + 4(3x4-1x1) = 3(-11) - 2(0) + 4(11) = -33+44 = 11.
(ii) |B| = 4(5x4-2x1) - 2(1x4-2x2) + 2(1x1-5x2) = 4(18) - 2(0) + 2(-9) = 72-0-18 = 54.
(b) Using cofactors and the adjoint method: Adj(A) is computed from the matrix of cofactors (transposed), and A^-1 = (1/|A|) x Adj(A) = (1/11) x Adj(A), giving the inverse matrix scaled by 1/11.

NECO Mathematics 2007 Theory — Question 6

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