https://file.aiquickdraw.com/mathbot/file/17259620477874fa72fyp.jpg

The problem in the image appears to involve multiplying a vector by a matrix. The expression is:

\[
(2 \; -1) \begin{pmatrix} 1 & 2 & 3 \\ 1 & -1 & 4 \end{pmatrix}
\]

We have a row vector \((2, -1)\) and a matrix:

\[
\begin{pmatrix} 1 & 2 & 3 \\ 1 & -1 & 4 \end{pmatrix}.
\]

To find the result, we perform matrix multiplication between the row vector and the matrix. The operation is defined as follows:

\[
(2, -1) \times \begin{pmatrix} 1 & 2 & 3 \\ 1 & -1 & 4 \end{pmatrix} = (2 \cdot 1 + (-1) \cdot 1, \; 2 \cdot 2 + (-1) \cdot (-1), \; 2 \cdot 3 + (-1) \cdot 4).
\]

Let's compute each term step-by-step:

1. **First element:** \(2 \cdot 1 + (-1) \cdot 1 = 2 - 1 = 1\)
2. **Second element:** \(2 \cdot 2 + (-1) \cdot (-1) = 4 + 1 = 5\)
3. **Third element:** \(2 \cdot 3 + (-1) \cdot 4 = 6 - 4 = 2\)

Thus, the resulting vector is:

\[
(1, 5, 2).
\]

### Final Answer:
\[
(2, -1) \times \begin{pmatrix} 1 & 2 & 3 \\ 1 & -1 & 4 \end{pmatrix} = (1, 5, 2).
\]

Would you like a detailed explanation of matrix multiplication or have any other questions?

Here are 5 related questions you might find interesting:
1. How do you multiply a column vector by a matrix?
2. What are the properties of matrix multiplication?
3. How is matrix multiplication used in linear transformations?
4. Can a matrix be multiplied by another matrix of any size?
5. What is the determinant of a 2x2 matrix?

**Tip:** Remember that matrix multiplication is not commutative; \(AB \neq BA\) in general!

(2 -1) multiplied by the matrix [[1, 2, 3], [1, -1, 4]]

Learn how to multiply a row vector (2, -1) by a 2x3 matrix [[1, 2, 3], [1, -1, 4]] using matrix multiplication rules. Step-by-step solution suitable for students in Grades 9-12.

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