Skip to main content
Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblema 13d
Capitolo 7, Problema 13d

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B
Matrices A and B for exercise on matrix operations in college algebra course.

Guida verificata passo dopo passo
1
Step 1: Identify the matrices A and B given in the problem. Matrix A is \( \begin{bmatrix} 2 \\ -4 \\ 1 \end{bmatrix} \) and matrix B is \( \begin{bmatrix} -5 \\ 3 \\ -1 \end{bmatrix} \).
Step 2: Understand the operation to perform: \( -3A + 2B \). This means you will multiply each element of matrix A by -3 and each element of matrix B by 2.
Step 3: Multiply matrix A by -3. Multiply each element of A by -3: \( -3 \times 2 \), \( -3 \times -4 \), and \( -3 \times 1 \).
Step 4: Multiply matrix B by 2. Multiply each element of B by 2: \( 2 \times -5 \), \( 2 \times 3 \), and \( 2 \times -1 \).
Step 5: Add the resulting matrices from steps 3 and 4 element-wise. That is, add the corresponding elements from the two matrices to get the final matrix \( -3A + 2B \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Matrix Addition and Scalar Multiplication

Matrix addition involves adding corresponding elements of two matrices of the same dimensions. Scalar multiplication means multiplying every element of a matrix by a constant. These operations are fundamental for combining matrices as in the expression -3A + 2B.
Video consigliato:
03:42
Finding Zeros & Their Multiplicity

Matrix Dimensions and Compatibility

For matrix addition or subtraction, the matrices must have the same dimensions. Here, both A and B are 3x1 matrices, so operations like -3A + 2B are valid. Understanding dimensions ensures correct application of matrix operations.
Video consigliato:
4:35
Introduction to Matrices

Order of Operations in Matrix Expressions

When evaluating expressions like -3A + 2B, scalar multiplication is performed first on each matrix, followed by matrix addition. This order ensures accurate computation and avoids errors in combining matrices.
Video consigliato:
8:38
Performing Row Operations on Matrices
Pratica correlata
Domanda del libro di testo

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 \(\end{bmatrix}\)

99
views
Domanda del libro di testo

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

96
views
Domanda del libro di testo

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\(\end{bmatrix}\)

828
views
Domanda del libro di testo

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

114
views
Domanda del libro di testo

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

857
views
Domanda del libro di testo

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

89
views