Math Problem Statement
Matrix multiplication of two 2x2 matrices: [[2, 1], [3, 1]] and [[1, -1], [1, 1]]
Solution
To solve the given matrix multiplication problem:
You need to calculate the product of the two matrices:
2 & 1 \\ 3 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & -1 \\ 1 & 1 \end{bmatrix}$$ ### Step-by-Step Calculation: 1. **First row, first column:** $$(2 \cdot 1) + (1 \cdot 1) = 2 + 1 = 3$$ 2. **First row, second column:** $$(2 \cdot -1) + (1 \cdot 1) = -2 + 1 = -1$$ 3. **Second row, first column:** $$(3 \cdot 1) + (1 \cdot 1) = 3 + 1 = 4$$ 4. **Second row, second column:** $$(3 \cdot -1) + (1 \cdot 1) = -3 + 1 = -2$$ ### Final Result: $$\begin{bmatrix} 3 & -1 \\ 4 & -2 \end{bmatrix}$$ ### Correct Answer: Option **1**: $$\begin{bmatrix} 3 & -1 \\ 4 & -2 \end{bmatrix}$$ --- Let me know if you need further clarification or assistance! Here are 5 questions to expand your understanding: 1. How do you verify the result of a matrix multiplication? 2. What are the rules for dimensions of matrices to multiply them? 3. How can this problem be extended to 3x3 matrices? 4. What are real-life applications of matrix multiplication? 5. Can this problem be solved using programming? How? **Tip:** Practice multiplying matrices manually and double-checking your steps to build accuracy and confidence.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Multiplication
Linear Algebra
Matrix Operations
Formulas
Matrix multiplication formula: (A * B)_{ij} = Σ (A_ik * B_kj) for all k
Theorems
Matrix multiplication properties
Suitable Grade Level
Grades 9-12