Question

In Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write "not defined: $$ A=\left[\begin{array}{rrr} 0 & 3 & -5 \\ 1 & 2 & 6 \end{array}\right] \quad B=\left[\begin{array}{rrr} 4 & 1 & 0 \\ -2 & 3 & -2 \end{array}\right] \quad C=\left[\begin{array}{rr} 4 & 1 \\ 6 & 2 \\ -2 & 3 \end{array}\right] $$ $2 A+4 B$

Name: Problem 14, Chapter 8: College Algebra
Uploaded: 2023-02-21T17:46:25-08:00
Channel: Nicole Hoffman
Description: In Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write "not defined: 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 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write "not defined:
$$
A=\left[\begin{array}{rrr}
0 & 3 & -5 \\
1 & 2 & 6
\end{array}\right] \quad B=\left[\begin{array}{rrr}
4 & 1 & 0 \\
-2 & 3 & -2
\end{array}\right] \quad C=\left[\begin{array}{rr}
4 & 1 \\
6 & 2 \\
-2 & 3
\end{array}\right]
$$
$2 A+4 B$

College Algebra

Michael Sullivan 11th Edition

Chapter 8, Problem 14

Instant Answer

Solved by Expert Nicole Hoffman

02/21/2023

Step 1

This gives us: $2A = 2 \times \left[\begin{array}{rrr} 0 & 3 & -5 \\ 1 & 2 & 6 \end{array}\right] = \left[\begin{array}{rrr} 0 & 6 & -10 \\ 2 & 4 & 12 \end{array}\right]$ $4B = 4 \times \left[\begin{array}{rrr} 4 & 1 & 0 \\ -2 & 3 & -2 \end{array}\right] = Show more…

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In Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write "not defined: $$ A=\left[\begin{array}{rrr} 0 & 3 & -5 \\ 1 & 2 & 6 \end{array}\right] \quad B=\left[\begin{array}{rrr} 4 & 1 & 0 \\ -2 & 3 & -2 \end{array}\right] \quad C=\left[\begin{array}{rr} 4 & 1 \\ 6 & 2 \\ -2 & 3 \end{array}\right] $$ $2 A+4 B$

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Key Concepts

Matrix Addition

Matrix addition is the process of adding two matrices by adding their corresponding entries. For matrix addition to be defined, the matrices must have the same dimensions, meaning they must have the same number of rows and columns. This ensures that each element in one matrix has a corresponding element in the other.

Scalar Multiplication

Scalar multiplication involves multiplying every entry of a matrix by a scalar (a real number). This operation is linear and applied uniformly across all elements in the matrix. It simplifies expressions where matrices are scaled by constants before being added or subtracted.

Matrix Dimensions

Matrix dimensions refer to the number of rows and columns in a matrix. In operations such as addition and subtraction, it is essential that the matrices involved have identical dimensions. This compatibility condition ensures that each element from one matrix correctly aligns with its corresponding element in the other matrix.

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