In Problems 67-70, use a graphing utility to find the...

In Problems $67-70$, use a graphing utility to find the inverse, if it exists, of each matrix. Round answers to two decimal places.
$$\left[\begin{array}{rrr}
25 & 61 & -12 \\
18 & -2 & 4 \\
8 & 35 & 21
\end{array}\right]$$

Key Concepts

Matrix Inversion

Matrix inversion is the process of finding another matrix which, when multiplied with the original, results in the identity matrix. This is a fundamental concept in linear algebra used to solve systems of linear equations and understand linear transformations. The inverse of a matrix exists only if the matrix is square and its determinant is non-zero.

Determinant and Invertibility

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides critical information about the matrix, such as whether the matrix is invertible. A non-zero determinant indicates that the matrix has an inverse, while a zero determinant implies that the matrix is singular and therefore not invertible.

Graphing Utility

Graphing utilities, such as graphing calculators or computer algebra systems, are tools that can perform complex matrix operations including finding the inverse. They streamline the computation process, especially for larger matrices, by automating arithmetic and rounding tasks.

Numerical Rounding

Numerical rounding refers to the process of adjusting decimal values to a specified degree of precision. In the context of computing matrix inverses, rounding is often applied to manage the display of long decimal values, making the results easier to read and interpret without compromising significant numerical information.

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