Question

Use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists). $$\left[\begin{array}{rrrr}1& -2& -1& -2\\ 3& -5& -2& -3\\ 2& -5& -2& -5\\ -1& 4& 4& 11\end{array}\right]$$

Short answer

The inverse of a matrix can be found using a graphing utility, as long as the determinant of the matrix is not zero. The inverse of a matrix is the matrix that results in an identity matrix when multiplied by the original matrix.

Step-by-step solution

Check if Matrix is Invertible

Not all matrices have inverses. A matrix has an inverse if and only if its determinant is not zero. So, first compute the determinant of the given matrix. Use the matrix capabilities on the graphing utility to calculate the determinant. If the determinant is not zero, the matrix is invertible and you can proceed to the next step.

Calculate Matrix Inverse

If the given matrix is invertible, use the matrix capabilities of the graphing utility to calculate the inverse of the matrix. The graphing utility does this by performing row operations to transform the given matrix into an identity matrix. The same operations are then performed on an identity matrix to obtain the inverse.

Verify Result

To ensure that the calculated inverse is correct, multiply the given matrix by its calculated inverse. The result should be an identity matrix. If it is not, check the calculations.