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The problem involves performing matrix multiplication between the two given matrices. The first matrix is:

\[
\begin{bmatrix}
-1 & 6 & 6
\end{bmatrix}
\]

The second matrix is:

\[
\begin{bmatrix}
4 & -7 & -5 \\
-9 & -7 & 1 \\
2 & -1 & 7
\end{bmatrix}
\]

Matrix multiplication is possible when the number of columns in the first matrix equals the number of rows in the second matrix. In this case, the first matrix has 3 columns, and the second matrix has 3 rows, so the multiplication is possible.

To multiply these two matrices, we follow the standard process for matrix multiplication: multiply the corresponding elements from the row of the first matrix by the columns of the second matrix and sum them.

### Step-by-step multiplication:
We are multiplying the 1x3 matrix with the 3x3 matrix, which will result in a 1x3 matrix.

1. **First entry** (First row, first column):
\[
(-1 \times 4) + (6 \times -9) + (6 \times 2) = -4 + (-54) + 12 = -46
\]

2. **Second entry** (First row, second column):
\[
(-1 \times -7) + (6 \times -7) + (6 \times -1) = 7 + (-42) + (-6) = -41
\]

3. **Third entry** (First row, third column):
\[
(-1 \times -5) + (6 \times 1) + (6 \times 7) = 5 + 6 + 42 = 53
\]

### Final result:
The resulting matrix is:

\[
\begin{bmatrix}
-46 & -41 & 53
\end{bmatrix}
\]

If you have any questions or need further details, feel free to ask!

Here are some related questions:
1. How do you determine if two matrices can be multiplied?
2. What are the rules for matrix multiplication in terms of dimensions?
3. How would the result change if the matrices were transposed?
4. Can you explain what each element in the result represents?
5. What is the difference between matrix addition and multiplication?

**Tip:** When performing matrix multiplication, always double-check the dimensions to ensure compatibility before proceeding with the operation.

Perform the indicated matrix multiplication between [-1 6 6] and [[4 -7 -5], [-9 -7 1], [2 -1 7]].

Learn how to perform matrix multiplication between a 1x3 matrix and a 3x3 matrix, with a detailed step-by-step solution. This problem covers key concepts in matrix multiplication and linear algebra. Suitable for high school students in Grades 10-12.

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