Math Problem Statement
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]].
Solution
We are given the equation , where:
To solve for , we can rearrange the equation to isolate :
Now, let's calculate :
Next, subtract from :
Perform the subtraction element-wise:
= \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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Operations
Matrix Addition
Matrix Multiplication by a Scalar
Matrix Subtraction
Formulas
Matrix equation: X + 3A = B
Scalar multiplication: cA = c * A
Matrix subtraction: X = B - cA
Theorems
Properties of Matrix Addition
Properties of Scalar Multiplication
Suitable Grade Level
Grades 10-12