Math Problem Statement

What is the result of multiplying the matrix [[4, 2], [5, 3], [-1, 7]] with the vector [1, -1]?

Solution

The image depicts a matrix multiplication problem. The matrices involved are:

4 & 2 \\ 5 & 3 \\ -1 & 7 \end{pmatrix} \cdot \begin{pmatrix} 1 \\ -1 \end{pmatrix}$$ Let's multiply these matrices. The result of the multiplication will be a 3x1 matrix. Each element is calculated as follows: 1. **First Row:** $$4 \times 1 + 2 \times (-1) = 4 - 2 = 2$$ 2. **Second Row:** $$5 \times 1 + 3 \times (-1) = 5 - 3 = 2$$ 3. **Third Row:** $$-1 \times 1 + 7 \times (-1) = -1 - 7 = -8$$ So, the product of the matrices is: $$\begin{pmatrix} 2 \\ 2 \\ -8 \end{pmatrix}$$ Would you like further details or explanations? Here are five additional questions related to this topic: 1. What is the general process for multiplying two matrices? 2. How can matrix multiplication be applied in solving systems of linear equations? 3. What properties does matrix multiplication have, such as commutativity or associativity? 4. How does matrix multiplication differ from scalar multiplication? 5. What are some real-world applications of matrix multiplication? **Tip:** Always ensure the dimensions of the matrices are compatible for multiplication; the number of columns in the first matrix must equal the number of rows in the second matrix.

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Math Problem Analysis

Mathematical Concepts

Matrix Multiplication
Linear Algebra

Formulas

Matrix-Vector Multiplication Formula: For a matrix A and a vector x, the product is a new vector y, where y = A * x.

Theorems

Matrix Multiplication Rules: The number of columns in the matrix must equal the number of rows in the vector.

Suitable Grade Level

Grades 9-12