https://file.aiquickdraw.com/mathbot/file/1726109282174w4v1o5xq.jpg

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

\[
\begin{pmatrix}
0 & 3 \\
2 & 1
\end{pmatrix}
\]

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.

Solve the matrix multiplication problem of multiplying the row vector [2, -4] by a 2x2 matrix [[0, 3], [2, 1]]. This problem involves core concepts of linear algebra and matrix-vector multiplication, suitable for students in Grades 8-12.

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