Mathematics 2010 JAMB Past Questions - Question 27: If P= ,what is P¯¹ ?

Correct Answer

D

Explanation

=<2 -3> ,what is P¯¹ ? <1 1> det = -2(-3) = 5 co - factor <+1 +1> <-3 2> 6T <1 -3> <1 2> P¯¹ = 1/5 <1 +3> <-1 2> = <1/5 3/5> <1/5 2/5>To find the inverse of a 2x2 matrix P, denoted as P⁻¹, we can use the formula:P⁻¹ = (1 / det(P)) * adj(P)Where det(P) is the determinant of matrix P, and adj(P) is the adjugate of matrix P.Given matrix P = <2 -3>, we can calculate its determinant as follows:det(P) = (2 * 1) - (-3 * 1)      = 2 + 3      = 5Next, we need to find the adjugate of matrix P. The adjugate of a 2x2 matrix is obtained by swapping the elements on the main diagonal and changing the sign of the elements off the main diagonal. In this case, the adjugate of matrix P is:adj(P) = <1 3>Now, we can calculate the inverse of matrix P using the formula:P⁻¹ = (1 / det(P)) * adj(P)    = (1 / 5) * <1 3>    = <1/5 3/5>Therefore, the inverse of matrix P is P⁻¹ = <1/5 3/5>.