2) Perform the following operations on matrices. 9-5 4 (a) 7 3-6 1-5 4 4 3 8 7 -2 -1 9 62 (b)

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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## Matrix Operations

### Problem 2: Perform the following operations on matrices.

**(a)**  
Subtract the matrices:

\[
\begin{bmatrix}
9 & -5 & 4 \\
7 & 3 & -6 \\
1 & -5 & 4
\end{bmatrix}
-
\begin{bmatrix}
4 & 3 & 8 \\
7 & -2 & -1 \\
9 & 6 & 2
\end{bmatrix}
\]

**(b)**  
Multiply and add the matrices:

\[
-5 \cdot 
\begin{bmatrix}
3 & -2 \\
8 & 4
\end{bmatrix}
+
2 \cdot 
\begin{bmatrix}
9 & -1 \\
-1 & 3
\end{bmatrix}
\]

For (a), calculate each element in the resulting matrix by subtracting corresponding elements from the two matrices.

For (b), first multiply each element in the first matrix by -5, then multiply each element in the second matrix by 2, and finally add the two resulting matrices together.
Transcribed Image Text:## Matrix Operations ### Problem 2: Perform the following operations on matrices. **(a)** Subtract the matrices: \[ \begin{bmatrix} 9 & -5 & 4 \\ 7 & 3 & -6 \\ 1 & -5 & 4 \end{bmatrix} - \begin{bmatrix} 4 & 3 & 8 \\ 7 & -2 & -1 \\ 9 & 6 & 2 \end{bmatrix} \] **(b)** Multiply and add the matrices: \[ -5 \cdot \begin{bmatrix} 3 & -2 \\ 8 & 4 \end{bmatrix} + 2 \cdot \begin{bmatrix} 9 & -1 \\ -1 & 3 \end{bmatrix} \] For (a), calculate each element in the resulting matrix by subtracting corresponding elements from the two matrices. For (b), first multiply each element in the first matrix by -5, then multiply each element in the second matrix by 2, and finally add the two resulting matrices together.
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