https://file.aiquickdraw.com/mathbot/file/1727325342615ym2dxy4y.jpg

The problem asks to compute \( 5A - 5B \) where \( A \) and \( B \) are given matrices:

\[
A = \begin{bmatrix} 1 & 3 \\ -2 & 5 \\ 2 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & -1 \\ 4 & 1 \\ -1 & -5 \end{bmatrix}
\]

### Step 1: Multiply matrix \( A \) and \( B \) by 5
First, we'll compute \( 5A \) and \( 5B \) by multiplying each element of \( A \) and \( B \) by 5.

\[
5A = 5 \times \begin{bmatrix} 1 & 3 \\ -2 & 5 \\ 2 & 4 \end{bmatrix} = \begin{bmatrix} 5 & 15 \\ -10 & 25 \\ 10 & 20 \end{bmatrix}
\]
\[
5B = 5 \times \begin{bmatrix} 2 & -1 \\ 4 & 1 \\ -1 & -5 \end{bmatrix} = \begin{bmatrix} 10 & -5 \\ 20 & 5 \\ -5 & -25 \end{bmatrix}
\]

### Step 2: Subtract \( 5B \) from \( 5A \)

Now, subtract \( 5B \) from \( 5A \):

\[
5A - 5B = \begin{bmatrix} 5 & 15 \\ -10 & 25 \\ 10 & 20 \end{bmatrix} - \begin{bmatrix} 10 & -5 \\ 20 & 5 \\ -5 & -25 \end{bmatrix}
\]

This results in:

\[
5A - 5B = \begin{bmatrix} 5 - 10 & 15 - (-5) \\ -10 - 20 & 25 - 5 \\ 10 - (-5) & 20 - (-25) \end{bmatrix} = \begin{bmatrix} -5 & 20 \\ -30 & 20 \\ 15 & 45 \end{bmatrix}
\]

### Final Answer:

\[
5A - 5B = \begin{bmatrix} -5 & 20 \\ -30 & 20 \\ 15 & 45 \end{bmatrix}
\]

Would you like a detailed explanation of any step? 

Here are 5 questions related to the topic:

1. How do you perform scalar multiplication on a matrix?
2. What is matrix addition and subtraction?
3. What is the determinant of a matrix, and how is it calculated?
4. How can matrices be used to solve systems of linear equations?
5. What are the properties of matrix multiplication?

**Tip:** Always verify the dimensions of matrices when performing operations like addition or multiplication to ensure they are compatible.

Given A = [[1, 3], [-2, 5], [2, 4]], B = [[2, -1], [4, 1], [-1, -5]], find 5A - 5B.

Learn how to solve the matrix equation 5A - 5B with given matrices A and B. This problem demonstrates key matrix operations like scalar multiplication and matrix subtraction. Ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation