https://file.aiquickdraw.com/mathbot/file/1726163544083hza0q6i9.jpg

We are given the equation \( X + 3A = B \), where:

\[
A = \begin{bmatrix} -2 & -1 \\ 1 & 0 \\ 3 & -4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & 3 \\ 2 & 0 \\ -4 & -1 \end{bmatrix}
\]

To solve for \( X \), we can rearrange the equation to isolate \( X \):

\[
X = B - 3A
\]

Now, let's calculate \( 3A \):

\[
3A = 3 \times \begin{bmatrix} -2 & -1 \\ 1 & 0 \\ 3 & -4 \end{bmatrix} = \begin{bmatrix} -6 & -3 \\ 3 & 0 \\ 9 & -12 \end{bmatrix}
\]

Next, subtract \( 3A \) from \( B \):

\[
X = \begin{bmatrix} 0 & 3 \\ 2 & 0 \\ -4 & -1 \end{bmatrix} - \begin{bmatrix} -6 & -3 \\ 3 & 0 \\ 9 & -12 \end{bmatrix}
\]

Perform the subtraction element-wise:

\[
X = \begin{bmatrix} 0 - (-6) & 3 - (-3) \\ 2 - 3 & 0 - 0 \\ -4 - 9 & -1 - (-12) \end{bmatrix}
= \begin{bmatrix} 6 & 6 \\ -1 & 0 \\ -13 & 11 \end{bmatrix}
\]

Thus, the solution is:

\[
X = \begin{bmatrix} 6 & 6 \\ -1 & 0 \\ -13 & 11 \end{bmatrix}
\]

This corresponds to the fourth option in the multiple-choice answers.

Would you like any additional details or explanations?

### Related Questions:
1. How do you multiply a matrix by a scalar?
2. Can you explain matrix subtraction in more detail?
3. What properties do matrix equations like \( X + 3A = B \) follow?
4. How can we check if the solution for \( X \) is correct?
5. What happens if \( A \) or \( B \) are not the same dimensions?

### Tip:
When solving matrix equations, always ensure the dimensions of the matrices match for addition and subtraction.

Solve for X in the equation X + 3A = B given A = [[-2, -1], [1, 0], [3, -4]] and B = [[0, 3], [2, 0], [-4, -1]].

Solve the matrix equation X + 3A = B with a step-by-step guide. Learn how to perform scalar multiplication and matrix subtraction. This problem involves basic matrix operations and is suitable for 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