What kinds of matrices do not have inverses?
Inverses of Matrices
Fractions are usually unavoidable when computing inverses.
By writing this system as a matrix equation you get:
If this were a normal linear equation where you had a constant times the variable equals a constant, you would multiply both sides by the multiplicative inverse of the coefficient. Do the same in this case.
All that is left is for you to substitute in and to perform the matrix multiplication to get the solution.
Earlier, you were asked what types of matrices do not have inverses. Non-square matrices do not generally have inverses. Square matrices that have determinants equal to zero do not have inverses.
Find the inverse of the following matrix.
This matrix is not invertible because its rows are not linearly independent. To test to see if a square matrix is invertible, check whether or not the determinant is zero. If the determinant is zero then the matrix is not invertible because the rows are not linearly independent.
Note that the rest of the entries turn out to be zero. This is left for you to confirm.
Being able to effectively use a calculator should improve your understanding of matrices and allow you to check all the work you do by hand.
The identity matrix happens to be its own inverse. Find another matrix that is its own inverse.
Find the inverse of each of the following matrices, if possible. Make sure to do some by hand and some with your calculator.
To see the Review answers, open this PDF file and look for section 8.9.