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Marina86 [1]
2 years ago
13

What is the inverse of

Mathematics
1 answer:
Paladinen [302]2 years ago
4 0

Answer:

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

Step-by-step 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} = \frac{1}{D} \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]

This gives:

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

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