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Find the inverses of the matrices in Exercises $1-4$ $$\left[\begin{array}{ll}{8} & {6} \\ {5} & {4}\end{array}\right]$$

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Algebra

Chapter 2

Matrix Algebra

Section 2

The Inverse of a Matrix

Introduction to Matrices

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Lectures

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01:22

Finding the Inverse of a M…

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Find the multiplicative in…

in this video, we're going to be calculating the inverse of the matrix A that we see displayed here. The first step in our computation is to find the determinant of this matrix a offer the determinant of a we look to the main diagonal. It's entries are eight and four, so we first take eight times for then we subtract the product of the off diagonal. The off diagonal is five and six. So right minus five times six then the result is going to be 32 minus 30. So we find that the determined of this matrix A is to now we're ready to state the inverse. We're going to use the formula since we have a two by two matrix displayed here that the inverse of this matrix A is equal to one over the determined of a provided the determinant is not zero. We have a value of two here multiplying a particular matrix. The way we find the Matrix is we look to the main Dagnall Britain and yellow and we interchange its values. So four goes in this position and eight goes in this position. Next, look to the off diagonal which contains elements five and six. They're going to stay put. But we take negative one times those elements. So negative five goes here and negative six goes here. So this becomes altogether 1/2, which is the determined of A and the Matrix. We multiply that by has entries for negative five and negative 68 So now we see that the inverse is equal to two negative five halves for the first column, then negative three and four for the second column. So this is how to calculate the inverse. But keep in mind that this information here is very important. It only works as a formula if this is a two by two matrix.

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