# Inverse of a 3x3 matrix

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## Inverting a 3x3 matrix using determinants Part 2: Adjugate matrix Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1

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Inverse operations are commonly used in algebra to simplify what otherwise might be difficult. For example, if a problem requires you to divide by a fraction, you can more easily multiply by its reciprocal. This is an inverse operation. Similarly, since there is no division operator for matrices, you need to multiply by the inverse matrix. Calculating the inverse of a 3x3 matrix by hand is a tedious job, but worth reviewing. You can also find the inverse using an advanced graphing calculator. To find the inverse of a 3x3 matrix, first calculate the determinant of the matrix.

(Note: also check out Matrix Inverse by Row Operations and the Matrix Calculator .) Step 1: calculating the Matrix of Minors,; Step 2: then turn that into the Matrix.
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If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Determinant of a 3x3 matrix: standard method 1 of 2. Determinant of a 3x3 matrix: shortcut method 2 of 2. Practice: Determinant of a 3x3 matrix. Inverting a 3x3 matrix using Gaussian elimination. Inverting a 3x3 matrix using determinants Part 1: Matrix of minors and cofactor matrix.

## Inverse of a 3 by 3 Matrix

If you're seeing this message, it means we're having trouble loading external resources on our website. - The inverse of a square matrix , sometimes called a reciprocal matrix, is a matrix such that.

## Inverting a 3x3 matrix using determinants Part 1: Matrix of minors and cofactor matrix

If we know this inverse, it's in general very useful. For example, it turns out that the inverse of the matrix. Knowing the inverse as we do, it is a simple matter to solve this system: we simply observe that. Unfortunately, for larger square matrices there does not exist any neat formula for the inverse. Indeed, finding inverses is so laborious that usually it's not worth the effort, and we use alternative methods for solving equation systems see Gaussian elimination. Just occasionally, however, it's worth it.

It needs 4 steps. It is all simple arithmetic but there is a lot of it, so try not to make a mistake! Here are the first two, and last two, calculations of the " Matrix of Minors " notice how I ignore the values in the current row and columns, and calculate the determinant using the remaining values :. This is easy! Just apply a "checkerboard" of minuses to the "Matrix of Minors". In other words, we need to change the sign of alternate cells, like this:. Now "Transpose" all elements of the previous matrix

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## Matrix Inverse

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How to Find the Inverse of a 3x3 Matrix. Inverse operations are commonly used in algebra to simplify what otherwise might be difficult. For example, if a problem.
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## 5 thoughts on “Inverse of a 3x3 matrix”

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Step 1: Matrix of Minors

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