Ch. 6 - Matrices and Determinants

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

Problem 9c

Chapter 7, Problem 9c

In Exercises 9 - 16, find the following matrices: c. - 4A

Verified step by step guidance

Identify matrix A as $ A = \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix} $.

Understand that multiplying a matrix by a scalar means multiplying each element of the matrix by that scalar.

Set up the scalar multiplication for $-4A$, which means multiply every element of matrix A by $-4$.

Multiply each element of matrix A by $-4$: $ -4 \times 4, -4 \times 1, -4 \times 3, -4 \times 2 $.

Write the resulting matrix with the new values in the same positions as in 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 each element scaled accordingly.

Matrix Representation and Notation

A matrix is a rectangular array of numbers arranged in rows and columns, denoted by brackets. Understanding how to read and write matrices, such as A = [[4,1],[3,2]], is essential for performing operations like addition, multiplication, and scalar multiplication.

Properties of Matrices

Matrices follow specific algebraic rules, such as distributive and associative properties. Recognizing these properties helps in manipulating matrices correctly, especially when combining operations like scalar multiplication and addition.

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Related Practice

Textbook Question

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

Textbook Question

In Exercises 9 - 16, find the following matrices: b. 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. $\begin{cases}\)w - 2x - y - 3z = -9 $\w$ + x - y = 0 \\3w + 4x + z = 6 \\2x - 2y + z = 3\(\end{cases}$

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Textbook Question

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

Textbook Question

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

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Textbook Question

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

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