Please it's just review practice number 2.3 number 8 not homework ### 2.3 Exercises**Instructions:** Unless otherwise specified, assume that all matrices in these exercises are $ n \times n $. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answers.1. \[ \begin{pmatrix} 5 & 7 \\ 3 & 6 \end{pmatrix} \]2. \[ \begin{pmatrix} 4 & 2 \\ 6 & -3 \end{pmatrix} \]3. \[ \begin{pmatrix} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & -4 \end{pmatrix} \]4. \[ \begin{pmatrix} 2 & 0 & 0 \\ 0 & 6 & 0 \\ 7 & 0 & 9 \end{pmatrix} \]5. \[ \begin{pmatrix} 5 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 4 & 2 \end{pmatrix} \]6. \[ \begin{pmatrix} 1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 6 & 9 \end{pmatrix} \]7. \[ \begin{pmatrix} 3 & 5 & 8 \\ 2 & 4 & 6 \\ 0 & 1 & 2 \end{pmatrix} \]8. \[ \begin{pmatrix} 0 & 4 & 7 & 4 \\ 0 & 0 & 5 & 8 \\ 1 & 0 & 7 & 4 \\ 2 & 0 & 6 & 5 \end{pmatrix} \]9. [Matrix image]10. [Matrix image]In Exercises 11 and 12, the matrices are all $ n \times n $.

The matrix, A is invertible if det(A)≠0.

Unless otherwise specified, assume that all matrices in these exercises are n xn. Determine which of the matrices in Exer- cises 1-10 are invertible. Use as few calculations as possible. Justify your answers.

Unless otherwise specified, assume that all matrices in these exercises are n xn. Determine which of the matrices in Exer- cises 1-10 are invertible. Use as few calculations as possible. Justify your answers.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Please it's just review practice number 2.3 number 8 not homework

### 2.3 Exercises

**Instructions:** Unless otherwise specified, assume that all matrices in these exercises are $ n \times n $. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answers.

1. \[
\begin{pmatrix}
5 & 7 \\
3 & 6
\end{pmatrix}
\]

2. \[
\begin{pmatrix}
4 & 2 \\
6 & -3
\end{pmatrix}
\]

3. \[
\begin{pmatrix}
3 & 0 & 0 \\
0 & 3 & 0 \\
0 & 0 & -4
\end{pmatrix}
\]

4. \[
\begin{pmatrix}
2 & 0 & 0 \\
0 & 6 & 0 \\
7 & 0 & 9
\end{pmatrix}
\]

5. \[
\begin{pmatrix}
5 & 0 & 1 \\
0 & 0 & 1 \\
0 & 4 & 2
\end{pmatrix}
\]

6. \[
\begin{pmatrix}
1 & 0 & 0 \\
0 & 3 & 0 \\
0 & 6 & 9
\end{pmatrix}
\]

7. \[
\begin{pmatrix}
3 & 5 & 8 \\
2 & 4 & 6 \\
0 & 1 & 2
\end{pmatrix}
\]

8. \[
\begin{pmatrix}
0 & 4 & 7 & 4 \\
0 & 0 & 5 & 8 \\
1 & 0 & 7 & 4 \\
2 & 0 & 6 & 5
\end{pmatrix}
\]

9. [Matrix image]

10. [Matrix image]

In Exercises 11 and 12, the matrices are all $ n \times n $.

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