https://file.aiquickdraw.com/mathbot/file/17273184379012oioae24.jpg

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

\[
\begin{pmatrix}
-1 \\
3 \\
-2
\end{pmatrix}
\cdot
\begin{pmatrix}
3 & -2
\end{pmatrix}
\]

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.

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

Learn how to multiply the column vector (-1, 3, -2) by the row vector (3, -2) to form a 3x2 matrix. This matrix multiplication problem covers key concepts of linear algebra and matrix operations. Suitable for students in Grades 10-12.

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