Math Problem Statement
Solve for x and y given the matrix equation:
\( \begin{bmatrix} x & -3 \\ 8 & 23 \end{bmatrix} = \begin{bmatrix} -5 & -3 \\ 8 & y \end{bmatrix} \)
Solution
To solve for and in this matrix equation:
we can equate corresponding elements from both matrices.
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For the top-left element:
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For the bottom-right element:
So, the solutions are:
Would you like a detailed explanation of each step or have any other questions?
Here are some related questions to expand your understanding:
- What are the basic properties of matrix equality?
- How do we handle equations when two matrices are set equal to each other?
- How can matrix equations be applied to solve systems of linear equations?
- What happens if the matrices are of different dimensions?
- Can matrices with variables in multiple positions be solved similarly?
Tip: When two matrices are equal, their corresponding elements must also be equal. This principle can simplify solving equations in matrix form.
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Math Problem Analysis
Mathematical Concepts
Matrix Equality
Algebra
Formulas
When two matrices are equal, their corresponding elements must also be equal
Theorems
Matrix Equality Property
Suitable Grade Level
Grades 10-12