Matrix Equation Solution: Solving for X in 2X = [1 -5; -4 6]

Math Problem Statement

Solve the matrix equation: [3 7; 2 4] + 2X = [1 -5; -4 6]

The equation in the image consists of a matrix equation involving three 2x2 matrices. Let's break it down:

$\begin{bmatrix} 3 & 7 \\ 2 & 4 \end{bmatrix} + 2X = \begin{bmatrix} 1 & -5 \\ -4 & 6 \end{bmatrix}$

We need to solve for the matrix $X$ .

Subtract the matrix on the left-hand side from both sides:

$2X = \begin{bmatrix} 1 & -5 \\ -4 & 6 \end{bmatrix} - \begin{bmatrix} 3 & 7 \\ 2 & 4 \end{bmatrix}$

= \begin{bmatrix} -2 & -12 \\ -6 & 2 \end{bmatrix}$$ ### Step 3: Divide by 2 Now divide the resulting matrix by 2 to find $$X$$: $$X = \frac{1}{2} \begin{bmatrix} -2 & -12 \\ -6 & 2 \end{bmatrix} = \begin{bmatrix} -1 & -6 \\ -3 & 1 \end{bmatrix}$$ So, the solution is: $$X = \begin{bmatrix} -1 & -6 \\ -3 & 1 \end{bmatrix}$$ Would you like a more detailed breakdown of any steps, or do you have any further questions? Here are some related questions for further practice: 1. How do you perform matrix multiplication? 2. What happens if the matrices aren't the same size in matrix addition or subtraction? 3. Can a scalar be multiplied by a non-square matrix? 4. How can we verify if two matrices are inverses of each other? 5. What are some practical applications of matrix operations in computer science? **Tip:** When performing matrix subtraction, always make sure to subtract corresponding elements from the same position in each matrix.

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Matrix Addition
Matrix Subtraction
Scalar Multiplication

Matrix Subtraction Formula: A - B = C where A, B, and C are matrices
Scalar Multiplication Formula: k * A where k is a scalar and A is a matrix

Matrix Subtraction Theorem
Scalar Multiplication Theorem

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