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The given problem involves multiplying two matrices. Let's break it down and solve it step by step.

The matrices are:
\[
A = \begin{pmatrix}
-8 & -9 & -8 \\
6 & 3 & 3
\end{pmatrix}
\]
and
\[
B = \begin{pmatrix}
3 \\
5 \\
7
\end{pmatrix}
\]

Matrix \(A\) has dimensions \(2 \times 3\), and matrix \(B\) has dimensions \(3 \times 1\). Matrix multiplication is possible because the number of columns in \(A\) (3) matches the number of rows in \(B\) (3).

To multiply \(A\) and \(B\), the result will be a \(2 \times 1\) matrix. Let's calculate it.

Each entry in the result is calculated by taking the dot product of the corresponding row in \(A\) with the column in \(B\). I'll compute it now.The matrix product of \(A\) and \(B\) is:

\[
\begin{pmatrix}
-125 \\
54
\end{pmatrix}
\]

This is the result of multiplying the two matrices. Let me know if you'd like further details or have any questions.

Here are 5 related questions you could explore:
1. How do you verify if two matrices can be multiplied?
2. What are the dimensions of the product of two matrices?
3. How would matrix multiplication differ for square matrices?
4. What applications can matrix multiplication have in physics or economics?
5. Can you multiply two matrices if their dimensions are \(3 \times 2\) and \(2 \times 4\)?

**Tip:** When multiplying matrices, always ensure the number of columns in the first matrix matches the number of rows in the second matrix to make the multiplication valid.

Find the following matrix product: A = [[-8, -9, -8], [6, 3, 3]] and B = [[3], [5], [7]].

Learn how to multiply a 2x3 matrix by a 3x1 matrix with a step-by-step solution. This problem involves calculating the product of matrices A = [[-8, -9, -8], [6, 3, 3]] and B = [[3], [5], [7]], resulting in a 2x1 matrix. Suitable for students in Grades 10-12.

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