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$$  $$COMPUTE the following matrix vector product

It seems that the text extraction did not succeed. Let me directly interpret the mathematical content visible in the image you uploaded.

The given objects are:

\[
A = 
\begin{pmatrix}
-5 & 2 & 1 & -4 \\
-1 & 0 & -4 & -4 \\
2 & -4 & -4 & -3 
\end{pmatrix}
\quad \text{and} \quad
\mathbf{x} = 
\begin{pmatrix}
4 \\
-7 \\
-7 \\
-8 
\end{pmatrix}
\]

We need to compute the matrix-vector product $ A \cdot \mathbf{x} $. Let's proceed step-by-step.

---

\[
\mathbf{y} = A \cdot \mathbf{x}
\]

Each entry of the result vector $ \mathbf{y} $ is computed as the dot product of the corresponding row of $ A $ with the vector $ \mathbf{x} $. 

Let me compute this for you.The matrix-vector product $ A \cdot \mathbf{x} $ results in:

\[
\mathbf{y} = 
\begin{pmatrix}
-9 \\
56 \\
88 
\end{pmatrix}
\]

This means that multiplying the matrix $ A $ by the vector $ \mathbf{x} $ yields the vector $ \mathbf{y} = [-9, 56, 88]^T $.

---

Would you like me to:

1. Verify the steps of the dot product in detail for each entry?
2. Explain how matrix-vector multiplication works conceptually?
3. Show how to perform this multiplication using another method (like element-wise computation)?
4. Describe common applications of matrix-vector multiplication?
5. Assist with checking if the system $ A \cdot \mathbf{x} = \mathbf{b} $ has any solutions, given a specific vector $ \mathbf{b} $?

**Tip:** When multiplying a matrix by a vector, ensure that the number of columns in the matrix matches the size of the vector.

COMPUTE the following matrix vector product

Learn how to compute the matrix-vector product of matrix A and vector x with a detailed step-by-step solution. This problem involves key linear algebra concepts, including matrix-vector multiplication and the dot product definition. Suitable for students in Grades 10-12.

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