Math Problem Statement
Evaluate the sum of the following matrices:
\[
\begin{bmatrix} 9 & 8 \\ -1 & 0 \end{bmatrix} +
\begin{bmatrix} 0 & 4 \\ -3 & -1 \end{bmatrix} +
\begin{bmatrix} -13 & -9 \\ 4 & -1 \end{bmatrix}.\]
Solution
To evaluate the given matrix expression:
The matrices are:
\begin{bmatrix} 0 & 4 \\ -3 & -1 \end{bmatrix} + \begin{bmatrix} -13 & -9 \\ 4 & -1 \end{bmatrix}.$$ ### Step-by-step solution: 1. **Add corresponding elements of the matrices:** Add elements in the same positions across all three matrices. - **(1,1) position:** $$9 + 0 + (-13) = -4$$ - **(1,2) position:** $$8 + 4 + (-9) = 3$$ - **(2,1) position:** $$-1 + (-3) + 4 = 0$$ - **(2,2) position:** $$0 + (-1) + (-1) = -2$$ 2. **Resulting matrix:** $$\begin{bmatrix} -4 & 3 \\ 0 & -2 \end{bmatrix}.$$ ### Final Answer: $$\begin{bmatrix} -4 & 3 \\ 0 & -2 \end{bmatrix}.$$ --- Would you like further details or clarification? --- Here are 5 related questions to deepen your understanding: 1. How can matrix addition be used in real-world applications like data processing? 2. What are the properties of matrix addition, and how do they differ from matrix multiplication? 3. Can matrix addition be performed on matrices with different dimensions? Why or why not? 4. How would scalar multiplication affect each element of a matrix before addition? 5. What happens when you add the zero matrix to another matrix? **Tip:** Always ensure matrices are of the same dimension before adding them element-wise!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Addition
Formulas
Matrix addition: Add corresponding elements of matrices
Theorems
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Suitable Grade Level
Grades 8-10