Matrix Multiplication: Row Vector by 2x2 Matrix

Math Problem Statement

[2, -4] × [ [0, 3], [2, 1] ]

The image displays a matrix multiplication problem. The goal is to multiply the row vector $[2, -4]$ by the matrix:

0 & 3 \\ 2 & 1 \end{pmatrix}$$ Let's solve the matrix multiplication step by step: 1. Multiply the row vector $$[2, -4]$$ by the first column of the matrix: $$(2 \times 0) + (-4 \times 2) = 0 - 8 = -8$$ 2. Multiply the row vector $$[2, -4]$$ by the second column of the matrix: $$(2 \times 3) + (-4 \times 1) = 6 - 4 = 2$$ Thus, the result of the matrix multiplication is: $$\begin{pmatrix} -8 \\ 2 \end{pmatrix}$$ The correct answer is $$[-8, 2]$$. Would you like further details on the matrix multiplication process or have any other questions? Here are five related questions to expand your knowledge: 1. How do you multiply a matrix by a vector? 2. What are the conditions for matrix multiplication to be possible? 3. Can matrix multiplication be done in any order? 4. What is the geometric interpretation of matrix-vector multiplication? 5. How does matrix multiplication change with larger matrices? **Tip:** Matrix multiplication is not commutative, meaning the order in which matrices are multiplied matters.

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Matrix Multiplication
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General Matrix Multiplication Rule

Matrix Multiplication Theorem

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