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 20
Capitolo 7, Problema 20

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. -5(A+D)

Guida verificata passo dopo passo
1
Step 1: Understand the problem. The problem involves performing matrix operations. You are tasked with calculating -5(A + D), where A and D are matrices. Ensure that the matrices A and D are defined and have the same dimensions, as matrix addition is only defined for matrices of the same size.
Step 2: Add the matrices A and D. To do this, add the corresponding elements of matrices A and D. For example, if A = [[a11, a12], [a21, a22]] and D = [[d11, d12], [d21, d22]], then A + D = [[a11 + d11, a12 + d12], [a21 + d21, a22 + d22]].
Step 3: Multiply the resulting matrix (A + D) by the scalar -5. To perform scalar multiplication, multiply each element of the matrix (A + D) by -5. For example, if A + D = [[x11, x12], [x21, x22]], then -5(A + D) = [[-5 * x11, -5 * x12], [-5 * x21, -5 * x22]].
Step 4: Verify your calculations. Double-check that the addition of matrices A and D was performed correctly and that each element of the resulting matrix was multiplied by -5 accurately.
Step 5: If the dimensions of A and D are not the same, state that the operation is not defined because matrix addition requires matrices to have the same dimensions.

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

Matrix addition involves combining two matrices of the same dimensions by adding their corresponding elements. For example, if A and D are both 2x2 matrices, the sum A + D is obtained by adding each element in A to the corresponding element in D. This operation is only defined when the matrices have the same size.
Video consigliato:
8:38
Performing Row Operations on Matrices

Scalar Multiplication

Scalar multiplication refers to the process of multiplying each element of a matrix by a scalar (a single number). In the expression -5(A + D), the result of the matrix addition A + D is multiplied by -5, which scales each element of the resulting matrix by -5. This operation is defined for any matrix regardless of its dimensions.
Video consigliato:
03:42
Finding Zeros & Their Multiplicity

Matrix Dimensions

Matrix dimensions describe the size of a matrix in terms of rows and columns, denoted as 'm x n' where m is the number of rows and n is the number of columns. Understanding dimensions is crucial for determining whether matrix operations, such as addition or multiplication, can be performed. If A and D have different dimensions, the operation A + D would be undefined.
Video consigliato:
4:35
Introduction to Matrices
Pratica correlata
Domanda del libro di testo

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. {w+x−y+z=−22w−x+2y−z=7−w+2x+y+2z=−1\(\begin{cases}\) w + x - y + z = -2 \\ 2w - x + 2y - z = 7 \\ -w + 2x + y + 2z = -1 \(\end{cases}\)

658
views
Domanda del libro di testo

For Exercises 11–22, use Cramer's Rule to solve each system. {2x=3y+25x=51−4y\(\begin{cases}\) 2x = 3y + 2 \\ 5x = 51 - 4y \(\end{cases}\)

806
views
Domanda del libro di testo

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. {x+y−2z=23x−y−6z=−7\(\begin{cases}\) x + y - 2z = 2 \\ 3x - y - 6z = -7 \(\end{cases}\)

670
views
Domanda del libro di testo

Let A=[−3−72−950]A = \(\begin{bmatrix}\) -3 & -7 \\ 2 & -9 \\ 5 & 0 \(\end{bmatrix}\) and B=[−5−1003−4]B = \(\begin{bmatrix}\) -5 & -1 \\ 0 & 0 \\ 3 & -4 \(\end{bmatrix}\). Solve each matrix equation for X. 2X + A = B

855
views
Domanda del libro di testo

Let A=[−3−72−950]A = \(\begin{bmatrix}\) -3 & -7 \\ 2 & -9 \\ 5 & 0 \(\end{bmatrix}\) and B=[−5−1003−4]B = \(\begin{bmatrix}\) -5 & -1 \\ 0 & 0 \\ 3 & -4 \(\end{bmatrix}\). Solve each matrix equation for X. 3X + 2A = B

104
views
Domanda del libro di testo

For Exercises 11–22, use Cramer's Rule to solve each system. {3x−4y=42x+2y=12\(\begin{cases}\) 3x - 4y = 4 \\ 2x + 2y = 12 \(\end{cases}\)

798
views