https://file.aiquickdraw.com/mathbot/file/1726801668636dhlzhu2r.jpg

The problem in the image asks to perform a matrix-vector multiplication. The given matrix and vector are:

\[
\begin{pmatrix}
5 & 4 & 2 \\
4 & 2 & 3
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2 \\
x_3
\end{pmatrix}
\]

The multiplication can be done as follows:

- First row of the matrix:
\[
(5 \times x_1) + (4 \times x_2) + (2 \times x_3)
\]

- Second row of the matrix:
\[
(4 \times x_1) + (2 \times x_2) + (3 \times x_3)
\]

Thus, the result is a 2x1 column vector:

\[
\begin{pmatrix}
5x_1 + 4x_2 + 2x_3 \\
4x_1 + 2x_2 + 3x_3
\end{pmatrix}
\]

If you have any further questions or need more details, feel free to ask!

Here are five related questions for practice:
1. How do you determine the dimensions of a matrix product?
2. What conditions must be met for two matrices to be multiplied?
3. Can you perform a dot product between a row vector and a column vector?
4. What happens when you multiply two square matrices?
5. What are the properties of matrix multiplication (e.g., is it commutative)?

**Tip:** Always verify that the dimensions of your matrices match appropriately before multiplying. For matrix-vector multiplication, the number of columns in the matrix must equal the number of elements in the vector.

Perform the indicated matrix operation: Multiply the 2x3 matrix by the 3x1 vector.

Learn how to multiply a 2x3 matrix by a 3x1 vector. This problem demonstrates key concepts of linear algebra, including matrix-vector multiplication and how to compute a 2x1 result using the row-by-column method.

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