In Exercises 23–26, use the matrix capabilities of a...

In Exercises 23–26, use the matrix capabilities of a graphing utility to evaluate the expression.
$$\frac{11}{25}\left[\begin{array}{rr}
2 & 5 \\
-1 & -4
\end{array}\right]+6\left[\begin{array}{rr}
-3 & 0 \\
2 & 2
\end{array}\right]$$

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Key Concepts

Using Graphing Utility for Matrix Evaluation

Graphing utilities and computer algebra systems offer matrix capabilities that streamline operations like scalar multiplication and addition. These tools allow users to input matrices directly and perform complex calculations efficiently, minimizing manual errors and enhancing understanding of matrix operations in a practical, computational context.

Matrix Scalar Multiplication

In linear algebra, multiplying a matrix by a scalar involves multiplying each entry of the matrix by that scalar. This operation scales the entire matrix uniformly and is an essential operation for adjusting the magnitude of a matrix without changing its direction, similar to multiplying a vector by a scalar.

Matrix Addition

Matrix addition is the process of adding two matrices by summing corresponding entries. It is a fundamental operation in matrix algebra and requires that the matrices have the same dimensions. This operation is used to combine matrices and is essential for various applications such as solving systems of linear equations and transformations.

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