Obe dari matriks -3 0 -1_2 0 0_2 0 0*x1_x2_x3

Let's break down the matrix multiplication problem you've given. Based on your description, we have:

The matrix:

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

And the vector:

\[
\begin{bmatrix}
x_1 \\
x_2 \\
x_3
\end{bmatrix}
\]

To multiply the matrix by the vector, we perform the dot product of each row of the matrix with the vector. 

### First Row:
\[
(-3) \cdot x_1 + 0 \cdot x_2 + (-1) \cdot x_3 = -3x_1 - x_3
\]

### Second Row:
\[
2 \cdot x_1 + 0 \cdot x_2 + 0 \cdot x_3 = 2x_1
\]

### Third Row:
\[
2 \cdot x_1 + 0 \cdot x_2 + 0 \cdot x_3 = 2x_1
\]

### Final Result:
\[
\begin{bmatrix}
-3x_1 - x_3 \\
2x_1 \\
2x_1
\end{bmatrix}
\]

This is the result of the matrix multiplication.

Would you like further details or explanations on any part? Here are 5 related questions to expand the topic:

1. How do you compute the determinant of a matrix?
2. How do you find the inverse of a matrix?
3. What are some applications of matrix multiplication in real-world problems?
4. How do eigenvalues and eigenvectors relate to matrices?
5. What is the rank of a matrix and how is it determined?

**Tip:** When multiplying matrices, ensure that the number of columns in the first matrix matches the number of rows in the second matrix for the operation to be valid.

Understand the matrix-vector multiplication of the 3x3 matrix [-3, 0, -1; 2, 0, 0; 2, 0, 0] with the vector [x1, x2, x3]. This detailed solution covers key concepts in linear algebra, perfect for students in Grades 10-12.

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