Math Problem Statement

Solve for X in the matrix equation: [-9 6 -1; 5 1 3] = -4X + 5[-1 -9 -2; 6 6 -4]

Solution

The solution to the matrix equation is:

1 & -\frac{51}{4} & -\frac{9}{4} \\ \frac{25}{4} & \frac{29}{4} & -\frac{23}{4} \end{bmatrix}$$ Do you want further details or have any questions? Here are some related questions to expand your understanding: 1. How can you verify the solution by substituting it back into the original matrix equation? 2. What are the steps involved in solving systems of matrix equations like this one? 3. How do matrix operations such as scalar multiplication and matrix addition work? 4. Can this system of equations be solved using Gaussian elimination? 5. What are the real-life applications of solving matrix equations like this? **Tip**: When working with matrices, always check if they are compatible for operations like addition, multiplication, and inversion.

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Matrix Equation Solving

Formulas

AX = B
Scalar multiplication
Matrix addition

Theorems

Matrix addition and scalar multiplication rules
Matrix equation solving using inverse or elimination

Suitable Grade Level

Undergraduate

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