Multiply the matrices.
(a)

3	4	5

4

5
7

The given matrices seem to be:

Matrix A:
\[
\begin{pmatrix}
3 & 4 & 5
\end{pmatrix}
\]
Matrix B:
\[
\begin{pmatrix}
4 \\
5 \\
7
\end{pmatrix}
\]

To multiply these matrices, we perform matrix multiplication. Matrix A is a \(1 \times 3\) matrix, and Matrix B is a \(3 \times 1\) matrix. The resulting matrix will be a \(1 \times 1\) matrix (since we're multiplying a \(1 \times 3\) by a \(3 \times 1\)).

The multiplication is carried out as follows:

\[
\text{Result} = (3 \times 4) + (4 \times 5) + (5 \times 7)
\]

Now, let's compute this:

\[
= 12 + 20 + 35 = 67
\]

Thus, the result of the matrix multiplication is:

\[
\begin{pmatrix}
67
\end{pmatrix}
\]

Would you like a detailed explanation of matrix multiplication, or do you have any other questions?

### Related questions:
1. What happens if we multiply a \(3 \times 1\) matrix by a \(1 \times 3\) matrix?
2. Can matrix multiplication always be performed between any two matrices?
3. What are the rules of dimensions in matrix multiplication?
4. How do we multiply larger matrices, such as \(3 \times 3\) by \(3 \times 3\)?
5. How is matrix multiplication used in solving systems of linear equations?

**Tip:** When performing matrix multiplication, always check the dimensions first! The number of columns in the first matrix must match the number of rows in the second matrix.

Learn how to multiply a 1x3 matrix by a 3x1 matrix with a detailed step-by-step solution. This problem demonstrates matrix multiplication by computing the dot product of corresponding elements. Suitable for students in Grades 9-12 studying linear algebra concepts.

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