https://file.aiquickdraw.com/mathbot/file/1726449670927zm58t8qs.jpg

The image shows a matrix multiplication problem involving two matrices. The first matrix \( B \) appears to be a row vector:

\[
B = \begin{bmatrix} 4 & 3 & 5 \end{bmatrix}
\]

The second matrix \( C \) is a 3x3 matrix:

\[
C = \begin{bmatrix}
5 & 2 & 9 \\
5 & 4 & 6 \\
3 & 1 & 5
\end{bmatrix}
\]

The problem asks for the product \( BC \). This involves multiplying the row vector \( B \) by the matrix \( C \).

### Matrix multiplication process:

To compute \( BC \), we perform the dot product of the row vector with each column of matrix \( C \).

\[
BC = \begin{bmatrix} 
(4 \times 5 + 3 \times 5 + 5 \times 3) & (4 \times 2 + 3 \times 4 + 5 \times 1) & (4 \times 9 + 3 \times 6 + 5 \times 5)
\end{bmatrix}
\]

Let me calculate each element:

1. First element: \( 4 \times 5 + 3 \times 5 + 5 \times 3 = 20 + 15 + 15 = 50 \)
2. Second element: \( 4 \times 2 + 3 \times 4 + 5 \times 1 = 8 + 12 + 5 = 25 \)
3. Third element: \( 4 \times 9 + 3 \times 6 + 5 \times 5 = 36 + 18 + 25 = 79 \)

Thus, the result of the multiplication \( BC \) is:

\[
BC = \begin{bmatrix} 50 & 25 & 79 \end{bmatrix}
\]

Would you like a more detailed explanation or further help? 

Here are 5 questions that can expand this information:

1. What are the rules for matrix multiplication?
2. How does matrix multiplication apply to vectors?
3. What are some applications of matrix multiplication in real-world problems?
4. Can matrix multiplication be used in solving systems of linear equations?
5. How does matrix multiplication differ from element-wise multiplication?

**Tip:** When multiplying matrices, the number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be valid.

Perform the matrix multiplication of B and C as shown in the image. B is a row vector [4, 3, 5] and C is a 3x3 matrix with columns [5, 5, 3], [2, 4, 1], [9, 6, 5].

Learn how to multiply a 1x3 row vector B = [4, 3, 5] by a 3x3 matrix C. Detailed steps include applying the matrix multiplication formula to find the resulting row vector BC = [50, 25, 79]. Suitable for students in Grades 9-12.

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