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Find the inverses of the matrices in Exercises $1-4$ $$\left[\begin{array}{ll}{3} & {-4} \\ {7} & {-8}\end{array}\right]$$

$\left[ \begin{array} { c c } { - 2 } & { 1 } \\ { - 7 / 4 } & { 3 / 4 } \end{array} \right]$

Algebra

Chapter 2

Matrix Algebra

Section 2

The Inverse of a Matrix

Introduction to Matrices

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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Find the inverses of the m…

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Find the inverse of each m…

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For the following exercise…

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we have the metric say given by three minus four seven minus eight. Since we have to complete its inverse, we start with computing is determinant. So the determinant of a he's given by the product off the elements on the main diagonal minus the product of the elements on the secondary diagonal. So on the main diner we have three times minus eight. Pay attention to the signs minus and on the second there that are gonna We have seven times minus for and it is minus 24 minus minus 28 which is blast for now. The inverse of a is given by one over its determinant that multiplies the metrics off then from a by swapping the elements on the men diagonal and negating the elements on the secondary diagonal. So the minus four becomes blast for and the seven becomes minus seven. Now we have already computed the determinant of A, which is four. So we can write. The final result as minus eight divided by four is minus two 45 before is one. Then we have minus seven over four and three over four

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