Math Problem Statement
Determine the x and y values of the following matrix similarities
[[4x -4], [-2y 5]] = [[-12 -4], [8 5]]
Answer:
4x= -12 x= -12/4 x= -3
-2y= 8 y= 8/-2 y= -4
Did you find my x and y values correctly?
Solution
Let’s verify your calculations step by step:
Given matrix equation:
4x & -4 \\ -2y & 5 \end{bmatrix} = \begin{bmatrix} -12 & -4 \\ 8 & 5 \end{bmatrix}$$ ### Step 1: Compare the elements of the two matrices element by element: #### Top-left element: $$4x = -12$$ Solve for $$x$$: $$x = \frac{-12}{4} = -3$$ Your value for $$x = -3$$ is **correct**. #### Bottom-left element: $$-2y = 8$$ Solve for $$y$$: $$y = \frac{8}{-2} = -4$$ Your value for $$y = -4$$ is **correct**. ### Final Answer: $$x = -3, \; y = -4$$ Your values for $$x$$ and $$y$$ are indeed correct! Do you have any further questions? Here are 5 related questions to explore further: 1. What does it mean for two matrices to be equal? 2. How can you verify other elements in the matrix match? 3. What are some applications of matrix equations in real-world problems? 4. Could $$x$$ and $$y$$ be complex numbers in other cases? 5. How would you solve this if the given equation involved matrix multiplication instead of equality? **Tip:** Always double-check element-wise comparisons when working with matrices to avoid small errors.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Equality
Linear Equations
Formulas
Element-wise equality: If A = B, then aᵢⱼ = bᵢⱼ
Theorems
Matrix equality property
Suitable Grade Level
Grades 9-11