Inverse to 3x3 matrix ```Name: michael j stevenson Status: N/A Age: N/A Location: N/A Country: N/A Date: Around 1995 ``` Question: How do you find the inverse of a 3x3 matrix? My Algebra II book does a wonderful job of explaining matrices in general and working with the determinant and inverse of 2x2 matrices, but it is very vague about 3x3. Although the book supplies us with the inverse if it is needed, I would like to know how to do it for myself. Replies: The reason that your book is so vague about the inverse of a three by three matrix is that they wanted to avoid the several pages of explanation needed to show how to find the inverse of a larger matrix. There are two commonly used methods. One uses determinants (you need to be able to find determi- nants of square matrices of size bigger than 2 by 2) and the other uses row operations. The second method is computationally the best. It may be time for some reading on your part. Try to find an easy reading linear algebra text. chaffer There are, of course, formulas for calculating the inverses of matrices of any size. In order to understand these formulas, you need to create some examples. So create a 3x3 matrix using algebra symbols for the entries. It will look like this: ``` a b c d e f g h i ``` Now write out the inverse matrix in terms of the 9 unknowns: rstuvwxyz. The product of the two matrices must give the matrix: ``` 1 0 0 0 1 0 0 0 1 ``` so you end up with 9 equations in 9 unknowns. So the formulas just give you a concise way of writing the solutions of these 9 equations. jlu Click here to return to the Mathematics Archives

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