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JAMB 2013 - Question 23

Mathematics 2013 JAMB Past Questions - Question 23: Find the inverse of 6 4

Find the inverse of <5 3> 6 4

A: <2 3/2,-3 -5/2>

B: <2 3/2,-3 5/2>

C: <2 -3/2,-3 -5/2>

D: <2 -3/2,-3 5/2>

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Correct Answer

Explanation

To find the inverse of a 2x2 matrix, we can use the formula:A^(-1) = (1/det(A)) * adj(A)Where A is the given matrix, det(A) is the determinant of A, and adj(A) is the adjugate of A.Given the matrix A = [[5, 3], [6, 4]], we can calculate its inverse as follows:Step 1: Calculate the determinant of Adet(A) = (5 * 4) - (3 * 6) = 20 - 18 = 2Step 2: Calculate the adjugate of AThe adjugate of A is obtained by swapping the elements in the main diagonal and changing the sign of the elements in the off-diagonal positions.adj(A) = [[4, -3], [-6, 5]]Step 3: Calculate the inverse of AA^(-1) = (1/2) * [[4, -3], [-6, 5]] = [[2, -3/2], [-3, 5/2]]Therefore, the inverse of the matrix A = [[5, 3], [6, 4]] is A^(-1) = [[2, -3/2], [-3, 5/2]].