https://file.aiquickdraw.com/mathbot/file/1725512745275b0qkkovr.jpg

The image you provided contains a matrix multiplication problem. Here's how we interpret it:

Matrix A:
\[
\begin{pmatrix}
1 & -4 & 3 \\
5 & 6 & 4
\end{pmatrix}
\]

Matrix B:
\[
\begin{pmatrix}
1 & 7 \\
3 & 1 \\
2 & 1
\end{pmatrix}
\]

Now, let's perform the multiplication of these two matrices \( A \times B \).

Matrix multiplication involves taking the dot product of rows from the first matrix with columns from the second matrix.

\[
C = A \times B = 
\begin{pmatrix}
(1 \times 1) + (-4 \times 3) + (3 \times 2) & (1 \times 7) + (-4 \times 1) + (3 \times 1) \\
(5 \times 1) + (6 \times 3) + (4 \times 2) & (5 \times 7) + (6 \times 1) + (4 \times 1)
\end{pmatrix}
\]

Now, I'll calculate each element.The result of the matrix multiplication \( A \times B \) is:

\[
C = 
\begin{pmatrix}
-5 & 6 \\
31 & 45
\end{pmatrix}
\]

Would you like further details or explanations about matrix multiplication?

Here are 5 related questions for practice:
1. How do you determine if two matrices can be multiplied?
2. What is the dot product of two vectors?
3. How would you multiply a 3x3 matrix with a 3x2 matrix?
4. What properties of matrix multiplication differ from regular number multiplication?
5. How can matrix multiplication be applied in solving systems of linear equations?

**Tip:** Matrix multiplication is not commutative, meaning \( A \times B \neq B \times A \) in general.

Multiply the matrices: 
Matrix A: 
[ [1, -4, 3], 
  [5, 6, 4] ] 
Matrix B: 
[ [1, 7], 
  [3, 1], 
  [2, 1] ]

Learn how to perform matrix multiplication of a 2x3 matrix and a 3x2 matrix. This problem involves key concepts in linear algebra, including the matrix multiplication formula and step-by-step calculations. Suitable for students in Grades 10-12.

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