Math Problem Statement

What is the result of multiplying the column vector (-1, 3, -2) by the row vector (3, -2)?

Solution

The problem shown in the image is a matrix multiplication between a column vector and a row vector. The vectors are:

-1 \\ 3 \\ -2 \end{pmatrix} \cdot \begin{pmatrix} 3 & -2 \end{pmatrix}$$ This type of multiplication results in a matrix where each element is the product of corresponding elements from the column vector and row vector. So, we will multiply each element in the column by each element in the row to form a 3x2 matrix. Let's calculate it: $$\begin{pmatrix} -1 \times 3 & -1 \times (-2) \\ 3 \times 3 & 3 \times (-2) \\ -2 \times 3 & -2 \times (-2) \end{pmatrix} = \begin{pmatrix} -3 & 2 \\ 9 & -6 \\ -6 & 4 \end{pmatrix}$$ So, the result of this multiplication is: $$\begin{pmatrix} -3 & 2 \\ 9 & -6 \\ -6 & 4 \end{pmatrix}$$ Would you like further clarification, or have any additional questions? Here are some related questions you might find useful: 1. What are the rules for matrix multiplication? 2. How do you multiply two matrices of different sizes? 3. What are the properties of matrix multiplication (associative, distributive, etc.)? 4. Can matrix multiplication be commutative? 5. How is matrix multiplication applied in solving systems of equations? **Tip**: When multiplying matrices, make sure the number of columns in the first matrix matches the number of rows in the second matrix.

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Math Problem Analysis

Mathematical Concepts

Matrix Multiplication
Linear Algebra

Formulas

Matrix multiplication rule: each element from the row of the first matrix is multiplied by the corresponding element from the column of the second matrix.

Theorems

Matrix multiplication properties: distributive, associative, but not commutative.

Suitable Grade Level

Grades 10-12