Chapter 4: Q7. (page 163)

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.
7.
$4 [\begin{matrix} 2 & 7 \\ - 3 & 6 \end{matrix}] + 5 [\begin{matrix} - 6 & - 4 \\ 3 & 0 \end{matrix}]$

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is

$4 [\begin{matrix} 2 & 7 \\ - 3 & 6 \end{matrix}] + 5 [\begin{matrix} - 6 & - 4 \\ 3 & 0 \end{matrix}] = [\begin{matrix} - 22 & 8 \\ 3 & 24 \end{matrix}]$

Step by step solution

- Define the concept used

Matrix subtraction and scalar multiplication:

If A and B are two matrices of order $m \times n$ , then the addition of the two matrices will also yield a matrix of order $m \times n$ wherein each element is the sum of the corresponding elements.

The product of a scalar k and an $m \times n$ matrix is an $m \times n$ matrix in which each element equals k times the corresponding elements of the original matrix.

- Perform the scalar multiplication first

Multiply each element in the first matrix $[\begin{matrix} 2 & 7 \\ - 3 & 6 \end{matrix}]$

by 4 and multiply each element in the second matrix $[\begin{matrix} - 6 & - 4 \\ 3 & 0 \end{matrix}]$

by 5.

$\begin{matrix} 4 [\begin{matrix} 2 & 7 \\ - 3 & 6 \end{matrix}] + 5 [\begin{matrix} - 6 & - 4 \\ 3 & 0 \end{matrix}] = [\begin{matrix} 4 (2) & 4 (7) \\ 4 (- 3) & 4 (6) \end{matrix}] + [\begin{matrix} 5 (- 6) & 5 (- 4) \\ 5 (3) & 5 (0) \end{matrix}] \\ = [\begin{matrix} 8 & 28 \\ - 12 & 24 \end{matrix}] + [\begin{matrix} - 30 & - 20 \\ 15 & 0 \end{matrix}] \end{matrix}$

- Add corresponding elements

Add corresponding elements of both the matrices $[\begin{matrix} 8 & 28 \\ - 12 & 24 \end{matrix}] + [\begin{matrix} - 30 & - 20 \\ 15 & 0 \end{matrix}]$ and simplify.

$\begin{matrix} 4 [\begin{matrix} 2 & 7 \\ - 3 & 6 \end{matrix}] + 5 [\begin{matrix} - 6 & - 4 \\ 3 & 0 \end{matrix}] = [\begin{matrix} 8 & 28 \\ - 12 & 24 \end{matrix}] + [\begin{matrix} - 30 & - 20 \\ 15 & 0 \end{matrix}] \\ = [\begin{matrix} 8 - 30 & 28 - 20 \\ - 12 + 15 & 24 + 0 \end{matrix}] \\ = [\begin{matrix} - 22 & 8 \\ 3 & 24 \end{matrix}] \end{matrix}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.
7.
$4 [\begin{matrix} 2 & 7 \\ - 3 & 6 \end{matrix}] + 5 [\begin{matrix} - 6 & - 4 \\ 3 & 0 \end{matrix}]$

Short Answer

Step by step solution

- Define the concept used

- Perform the scalar multiplication first

- Add corresponding elements

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.7.427−36+5−6−430

Short Answer

Step by step solution

- Define the concept used

- Perform the scalar multiplication first

- Add corresponding elements

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.
7.
$4 [\begin{matrix} 2 & 7 \\ - 3 & 6 \end{matrix}] + 5 [\begin{matrix} - 6 & - 4 \\ 3 & 0 \end{matrix}]$