2) Let A be Compute: tr(AA) 51 4 1 T (iv) (A^¹)" (v) AA² (vi)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
compute iv v & vi
![**Transcribed Image Text:**
2) Let \( A \) be
\[
\begin{bmatrix}
5 & 1 \\
4 & 1
\end{bmatrix}
\]
Compute:
(i) \, \( A^T \) \, \, \, \,
(ii) \, \( A^{-1} \) \, \, \, \,
(iii) \, \( (A^2)^{-1} \) \, \, \, \,
(iv) \, tr(AAT)
(v) \, \( (A^{-1})^T \)
(vi) \, \( A A^T \)
**Explanation:**
- **(i) \( A^T \)**: Transpose of matrix \( A \).
- **(ii) \( A^{-1} \)**: Inverse of matrix \( A \), if it exists.
- **(iii) \( (A^2)^{-1} \)**: Inverse of the matrix \( A \) squared, if it exists.
- **(iv) tr(AAT)**: Trace of the product of matrix \( A \) and its transpose.
- **(v) \( (A^{-1})^T \)**: Transpose of the inverse of matrix \( A \).
- **(vi) \( A A^T \)**: Product of matrix \( A \) and its transpose.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4035242d-f18b-4709-bb6e-951753bf8b42%2Ff1b1f7dc-6bc4-4b4c-863b-a5b30ccafff7%2F18410s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcribed Image Text:**
2) Let \( A \) be
\[
\begin{bmatrix}
5 & 1 \\
4 & 1
\end{bmatrix}
\]
Compute:
(i) \, \( A^T \) \, \, \, \,
(ii) \, \( A^{-1} \) \, \, \, \,
(iii) \, \( (A^2)^{-1} \) \, \, \, \,
(iv) \, tr(AAT)
(v) \, \( (A^{-1})^T \)
(vi) \, \( A A^T \)
**Explanation:**
- **(i) \( A^T \)**: Transpose of matrix \( A \).
- **(ii) \( A^{-1} \)**: Inverse of matrix \( A \), if it exists.
- **(iii) \( (A^2)^{-1} \)**: Inverse of the matrix \( A \) squared, if it exists.
- **(iv) tr(AAT)**: Trace of the product of matrix \( A \) and its transpose.
- **(v) \( (A^{-1})^T \)**: Transpose of the inverse of matrix \( A \).
- **(vi) \( A A^T \)**: Product of matrix \( A \) and its transpose.
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