What is the inverse of

Question

asked May 27, 2021 215k views

1 Answer

Lizziepika · Answer 1 · 2021-06-02T14:44:03+0000

Answer:

$A^(-1) = (1)/(66) \left[\begin{array}{cc}-2&-5\\6&-18\end{array}\right]$

Explanation:

Given

$A = \left[\begin{array}{cc}-18&5\\-6&-2\end{array}\right]$

Required

Determine the inverse

A matric is of the form:

$A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

First, we need to calculate the determinant (D)

D = a * d - b * c

By comparison, we have:

D = (-18 * -2) - (5 * -6)

D = (36) - (-30)

D = 36 +30

D = 66

The inverse is then represented as:

$A^(-1) = (1)/(D) \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]$

This gives:

$A^(-1) = (1)/(66) \left[\begin{array}{cc}-2&-5\\6&-18\end{array}\right]$