Mathematics 2011 JAMB Past Questions - Question 26: The inverse of matrix N ≤ 2 1> is 1 4

Correct Answer

B

Explanation

N = <2 3> <1 4>2 x 4 – 1 X 3 = 8 – 3 =5N¯¹ = 1/5 <4 -3> <-1 2>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 N:N = |2 1|      |1 4|To find the determinant of N:det(N) = (2 * 4) - (1 * 1) = 8 - 1 = 7Next, we need to find the adjugate of N:adj(N) = |4 -1|            |-1 2|Now, we can find the inverse of N:N^(-1) = (1/7) * |4 -1|                        |-1 2|Multiplying each element of the adjugate matrix by 1/7:N^(-1) = |4/7 -1/7|              |-1/7 2/7|Therefore, the inverse of the matrix N = |2 1| is |4/7 -1/7|.                                                                |-1/7 2/7|.