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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblem 15c
Chapter 7, Problem 15c

In Exercises 9 - 16, find the following matrices: c. - 4A
Matrices A and B for exercise 15 in college algebra, chapter on matrices and determinants.

Verified step by step guidance
1
Identify the matrix A given as [2-10-21412104-22].
Understand that the problem asks to find the matrix -4A, which means multiplying every element of matrix A by -4.
Multiply each element of matrix A by -4. For example, the element in the first row and first column (2) becomes -4 \(\times\) 2 = -8.
Apply this multiplication to all elements in matrix A to form the new matrix -4A.
Write the resulting matrix with all elements multiplied by -4, maintaining the same dimensions and order as matrix A.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix Scalar Multiplication

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). For example, multiplying matrix A by -4 means each entry in A is multiplied by -4, resulting in a new matrix with scaled values.
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Matrix Notation and Dimensions

Understanding matrix notation is essential; matrices are represented by brackets containing rows and columns. The dimensions (rows × columns) must be consistent for operations like addition or multiplication. Here, A and B are 3×3 matrices.
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Matrix Operations in Algebra

Matrix operations such as addition, subtraction, and scalar multiplication follow specific rules. These operations are foundational in algebra for solving systems, transformations, and more. Recognizing how to apply these rules is key to manipulating matrices correctly.
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Related Practice
Textbook Question

Use the fact that if A=[abcd]A=\(\begin{bmatrix}\)a & b\\ c & d\(\end{bmatrix}\), then A−1=1ad−bc[d−b−ca]A^{-1}=\(\frac{1}{ad-bc}\]\begin{bmatrix}\)d & -b\\ -c & a\(\end{bmatrix}\) to find the inverse of each matrix, if possible. Check that AA−1=I2AA^{-1} = I_2 and A−1A=I2A^{-1}A = I_2.

A=[10−2−51]A = \(\begin{bmatrix}\)10 & -2 \\-5 & 1\(\end{bmatrix}\)

Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. D-A

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Textbook Question

Use the fact that if A=[abcd]A = \(\begin{bmatrix}\) a & b \\ c & d \(\end{bmatrix}\), then A−1=1ad−bc[d−b−ca]A^{-1} = \(\frac{1}{ad-bc}\) \(\begin{bmatrix}\) d & -b \\ -c & a \(\end{bmatrix}\) to find the inverse of each matrix, if possible. Check that AA−1=I2AA^{-1} = I_2 and A−1A=I2A^{-1} A = I_2.

A=[3−1−42]A = \(\begin{bmatrix}\)3 & -1 \\-4 & 2\(\end{bmatrix}\)

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Textbook Question

In Exercises 9 - 16, find the following matrices: b. A - B

Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

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Textbook Question

In Exercises 9 - 16, find the following matrices: a. A + B