Which pair of matrices are inverses of each another?
Question
Answer:
if we put symbols for the numbers in the first matrix [tex] \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] [/tex]
to find the inverse of the first matrix
first we need to find the determinant (D)
D = ad - bc
a = 2, b = 3 , c = 6 and d = 8
D = 2x8 - 3x6
= 16 - 18
= -2
then to find the inverse we have to exchange a and d and also multiply b and c by -1
and divide all the terms in the matrix by determinant
inverse matrix is then
[tex] \left[\begin{array}{ccc} \frac{8}{-2} & \frac{-3}{-2} \\ \frac{-6}{-2} & \frac{2}{-2} \\\end{array}\right] [/tex]
simplified matrix, the answer of inverse matrix is
[tex] \left[\begin{array}{ccc}-4& \frac{3}{2} \\3&-1\\\end{array}\right] [/tex]
solved
general
10 months ago
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