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.
$$\left[\begin{array}{rrrr}
44 & 21 & 18 & 6 \\
-2 & 10 & 15 & 5 \\
21 & 12 & -12 & 4 \\
-8 & -16 & 4 & 9
\end{array}\right]$$

Key Concepts

Rounding and Precision

When using digital computation methods, results often need to be rounded to a specific number of decimal places to ensure clarity and usability. Rounding calculations, such as rounding to two decimal places, help in presenting a cleaner and more practical interpretation of the computed inverse matrix.

Graphing Utility for Matrix Operations

Graphing utilities, such as graphing calculators or computer algebra systems, provide efficient methods for performing matrix operations including finding the inverse. These tools are especially useful when dealing with larger matrices where manual computation is time-intensive and error-prone.

Matrix Inversion

Matrix inversion is the process of finding a matrix (called the inverse) that, when multiplied with the original matrix, results in the identity matrix. This concept is fundamental in linear algebra and is applicable to solving systems of linear equations, among other applications. An inverse exists only for square matrices that are non-singular, meaning they must have a non-zero determinant.

Determinant and Invertibility

The determinant is a scalar value that can be computed from a square matrix and indicates whether the matrix is invertible. A non-zero determinant implies the matrix is invertible, whereas a determinant of zero means the matrix does not have an inverse. This concept is key when determining if an inverse exists.

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