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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 14d
Chapter 7, Problem 14d

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B
Matrices A and B with values A = [6 2 -3], B = [4 -2 3] for matrix operations.

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Step 1: Understand the problem. You are asked to find the matrix expression -3A + 2B, where A and B are given matrices: A = [6 2 -3] and B = [4 -2 3].
Step 2: Multiply each element of matrix A by -3. This means you multiply each entry in A by -3, resulting in a new matrix: -3A = [-3*6 -3*2 -3*(-3)].
Step 3: Multiply each element of matrix B by 2. This means you multiply each entry in B by 2, resulting in a new matrix: 2B = [2*4 2*(-2) 2*3].
Step 4: Add the corresponding elements of the matrices -3A and 2B. This means you add the first element of -3A to the first element of 2B, the second element of -3A to the second element of 2B, and so on.
Step 5: Write the resulting matrix from the addition in step 4 as the final answer for -3A + 2B.

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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 each element of a matrix by a constant (scalar). For example, multiplying matrix A by -3 means each entry in A is multiplied by -3, resulting in a new matrix with scaled values.
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Matrix Addition and Subtraction

Matrix addition or subtraction requires matrices to have the same dimensions. Corresponding elements from each matrix are added or subtracted to form a new matrix. For instance, adding 2B to -3A means adding each element of 2B to the corresponding element of -3A.
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Matrix Representation and Notation

A matrix is a rectangular array of numbers arranged in rows and columns, denoted by brackets. Understanding the layout and notation of matrices A and B is essential to perform operations correctly, ensuring element-wise calculations align properly.
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Related Practice
Textbook Question

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

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Textbook Question

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

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. {4x−5y=172x+3y=3\(\begin{cases}\)4x - 5y = 17 \\2x + 3y = 3\(\end{cases}\)

Textbook Question

Perform each matrix row operation and write the new matrix.

[1−32∣031−1∣72−21∣3]−3R1+R2\(\begin{bmatrix}\)1 & -3 & 2 & \(\vert\) & 0 \\3 & 1 & -1 & \(\vert\) & 7 \\2 & -2 & 1 & \(\vert\) & 3\(\end{bmatrix}\]\quad\) -3R_1 + R_2

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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. {2x+y−z=23x+3y−2z=3\(\begin{cases}\)2x + y - z = 2 \\3x + 3y - 2z = 3\(\end{cases}\)

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Textbook Question

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

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