If A and B are matrices and AB = I, which of the following represents the value of B? A= [-1, 4 -3, 8]
Question
Answer:
if the product of 2 matrices are I this means that B is inverse matrix of A.the matrix A has been given
if we put symbols for the numbers in matrix A as shown below;
[tex] \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] [/tex]
we need to first find the determinant (D)
D = ad - bc
where a = -1 , b = 4, c = -3 and d = 8
substituting these values
D = -1x8 - (4x-3)
= -8 + 12 = 4
to find the inverse we need to exchange a and d and then multiply both b and c by -1
[tex] \left[\begin{array}{ccc}8&-4\\3&-1\\\end{array}\right] [/tex]
and then have to divide all the terms in matrix by determinant (4)
[tex]\left[\begin{array}{ccc} \frac{8}{4} & \frac{-4}{4} \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right][/tex]
the simplified inverse matrix B is;
[tex]\left[\begin{array}{ccc} 2 & -1 \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right][/tex]
solved
general
10 months ago
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