Dating matrix inverse books
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Math Inverse of a 3x3 Matrix Date: Sharon Wasson Subject: All it says is that the process is complicated and that students should use a computer or graphing calculator.
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I can find the determinant, use Cramer's Rule, and solve any other way - including the graphing calculator - but cannot dating matrix inverse books anything on this concept. I would at least like to see it even if I don't or can't use it. I like to use this method to find the inverse of a 3x3 or larger square matrix.
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Write the matrix, and to its right append an identity matrix of the same size. You'll have a 3x6 matrix.
Now operate on the matrix until the 3x3 left half is the identity matrix, by using elementary row operations. Then the 3x3 right half will be the inverse of the original matrix.
Elementary row operations are these: Multiply a row by a nonzero constant. Add a constant multiple of one row to another. Find the inverse of [-1 3 -3] [ 0 -6 5].
The Theory of Matrices; dating matrix inverse books
The explanation of this is that each elementary row dating matrix inverse books corresponds to multiplying a 3x3 matrix on the left: Now multiply on the left by carefully selected ones of these elementary operation matrices, according to the above procedure: Another approach is to let the 9 entries in the inverse matrix be unknowns, multiply the two matrices together, and set the result equal to the identity matrix.
That will get you a set of nine linear equations in nine unknowns which you can solve simultaneously.
You need to solve these for r, s, You can rearrange this system to see that it is actually three sets of simultaneous linear equations, each in three unknowns: You can solve them using Cramer's rule, if you like. That will give you r, s, An explicit formula for the inverse can also be given.
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Then the entire matrix is divided by d. It is a long exercise to verify that this works. If you need more help, feel free to write again.