Question

In Problems $9-24$, use the following matrices to evaluate the given expression. $A=\left[\begin{array}{rrr}0 & 3 & -5 \\ 1 & 2 & 6\end{array}\right] \quad B=\left[\begin{array}{rrr}4 & 1 & 0 \\ -2 & 3 & -2\end{array}\right] \quad C=\left[\begin{array}{rr}4 & 1 \\ 6 & 2 \\ -2 & 3\end{array}\right]$ $$2 A+4 B$$

Name: Problem 14, Chapter 8: College Algebra
Uploaded: 2021-05-21T03:06:17-08:00
Duration: 2 min 12 s
Channel: Nick Johnson
Description: In Problems 9-24, use the following matrices to evaluate the given expression. A=[ 0 3 -5 1 2 6 ] B=[ 4 1 0 -2 3 -2 ] C=[ 4 1 6 2 -2 3 ] 2 A+4 B

   In Problems $9-24$, use the following matrices to evaluate the given expression.
$A=\left[\begin{array}{rrr}0 & 3 & -5 \\ 1 & 2 & 6\end{array}\right] \quad B=\left[\begin{array}{rrr}4 & 1 & 0 \\ -2 & 3 & -2\end{array}\right] \quad C=\left[\begin{array}{rr}4 & 1 \\ 6 & 2 \\ -2 & 3\end{array}\right]$
$$2 A+4 B$$

College Algebra

Michael Sullivan 9th Edition

Chapter 8, Problem 14

Instant Answer

Solved by Expert Nick Johnson

05/21/2021

Step 1

This is done by multiplying every element in matrix $A$ by 2. So, we have: \[2A = 2 \times \left[\begin{array}{rrr}0 & 3 & -5 \\ 1 & 2 & 6\end{array}\right] = \left[\begin{array}{rrr}0 & 6 & -10 \\ 2 & 4 & 12\end{array}\right]\] Show more…

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In Problems $9-24$, use the following matrices to evaluate the given expression. $A=\left[\begin{array}{rrr}0 & 3 & -5 \\ 1 & 2 & 6\end{array}\right] \quad B=\left[\begin{array}{rrr}4 & 1 & 0 \\ -2 & 3 & -2\end{array}\right] \quad C=\left[\begin{array}{rr}4 & 1 \\ 6 & 2 \\ -2 & 3\end{array}\right]$ $$2 A+4 B$$

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Key Concepts

Matrix Operations

Matrix operations include various procedures such as addition, subtraction, and scalar multiplication. These operations form the basis of linear algebra and are essential for manipulating matrices in equations, systems, and transformations.

Scalar Multiplication

Scalar multiplication involves multiplying every element of a matrix by a constant value. This operation is used to scale a matrix and is distributive over matrix addition, allowing coefficients to be applied directly to matrices before combining them.

Matrix Addition

Matrix addition is the process of adding corresponding elements from two matrices of the same dimensions. It is a fundamental operation in linear algebra that combines matrices element-wise to produce a new matrix.

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