https://file.aiquickdraw.com/mathbot/file/172618108574438szofeq.jpg

The problem shown in the image is asking for the multiplication of two 2x2 matrices.

The matrices involved are:

\[
\begin{bmatrix}
4 & -3 \\
2 & -1
\end{bmatrix}
\quad \text{and} \quad
\begin{bmatrix}
x \\
-7
\end{bmatrix}
=
\begin{bmatrix}
17 \\
-3
\end{bmatrix}
\]

This is a matrix equation of the form:

\[
\begin{bmatrix}
4 & -3 \\
2 & -1
\end{bmatrix}
\begin{bmatrix}
x \\
-7
\end{bmatrix}
=
\begin{bmatrix}
17 \\
-3
\end{bmatrix}
\]

To solve this, we first perform the matrix multiplication:

1. First row: \( 4 \cdot x + (-3) \cdot (-7) = 4x + 21 \)
2. Second row: \( 2 \cdot x + (-1) \cdot (-7) = 2x + 7 \)

This gives us the system of equations:

\[
4x + 21 = 17
\]
\[
2x + 7 = -3
\]

Now, let's solve this system of equations.

### Solving the first equation:

\[
4x + 21 = 17
\]

Subtract 21 from both sides:

\[
4x = 17 - 21 = -4
\]

Divide by 4:

\[
x = \frac{-4}{4} = -1
\]

### Solving the second equation (for verification):

\[
2x + 7 = -3
\]

Subtract 7 from both sides:

\[
2x = -3 - 7 = -10
\]

Divide by 2:

\[
x = \frac{-10}{2} = -5
\]

There seems to be a contradiction in the solution. This suggests that the system of equations has no solution, meaning the matrices are inconsistent.

Let me know if you'd like further details or explanations!

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Here are 5 relative questions to explore this topic further:

1. How do you determine if a system of equations has no solution?
2. What are the properties of inconsistent systems in matrix equations?
3. How does matrix multiplication differ from scalar multiplication?
4. Can a matrix equation always be solved? Why or why not?
5. How can matrix inversion help in solving systems of linear equations?

**Tip:** When solving matrix equations, always check both equations to ensure consistency before concluding the solution!

Multiply the matrix [4 -3; 2 -1] with a vector matrix [x; -7] and find x, given the result is [17; -3].

Learn how to solve a 2x2 matrix multiplication problem where matrix A = [4 -3; 2 -1] and vector matrix B = [x; -7], with the result C = [17; -3]. Includes solving the system of linear equations.

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