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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 13c
Chapter 7, Problem 13c

In Exercises 9 - 16, find the following matrices: c. - 4A
Matrices A and B with values for college algebra exercise on matrix operations.

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1
Identify the matrix A given as [2-41].
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, multiply 2 by -4, -4 by -4, and 1 by -4.
Write the resulting matrix after multiplication, keeping the same dimensions as matrix A.
Verify that each element in the new matrix is correctly calculated as the product of -4 and the corresponding element in 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 given matrices A and B are 3x1 column matrices, meaning they have 3 rows and 1 column, which affects how operations like addition or multiplication are performed.
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Basic Matrix Operations

Matrix operations include addition, subtraction, and scalar multiplication. Knowing how to perform these operations correctly is crucial for solving problems involving matrices, such as finding -4A or combinations like 2 - 5B.
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Related Practice
Textbook Question

Find the following matrices: A+BA + B

A=[2−41],B=[−53−1]A = \(\begin{bmatrix}\)2 \\-4 \\1\(\end{bmatrix}\), B = \(\begin{bmatrix}\)-5 \\3 \\-1\(\end{bmatrix}\)

Textbook Question

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

Textbook Question

Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D

A=[2−1253−1]B=[0−2321−5]C=[123−112−121]D=[−2313−24]A=\(\begin{bmatrix}\)2 & -1 & 2\\ 5 & 3 & -1\(\end{bmatrix}\[\quad\) B=\(\begin{bmatrix}\)0 & -2\\ 3 & 2\\ 1 & -5\(\end{bmatrix}\)C=\(\begin{bmatrix}\)1 & 2 & 3\\ -1 & 1 & 2\\ -1 & 2 & 1\(\end{bmatrix}\]\quad\) D=\(\begin{bmatrix}\)-2 & 3 & 1\\ 3 & -2 & 4\(\end{bmatrix}\)

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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: a. A + B

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Textbook Question

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. {w−3x+y−4z=4−2w+x+2y=−23w−2x+y−6z=2−w+3x+2y−z=−6\(\begin{cases}\)w - 3x + y - 4z = 4 \\-2w + x + 2y = -2 \\3w - 2x + y - 6z = 2 \\-w + 3x + 2y - z = -6\(\end{cases}\)