1-Find the cosine of the angle between A and B with respect to the standard inner product on M22 2 4 A = (-²₁₂3) B = (-3² ₂) 1 4 2 2-Let A, B E M .Determine whether if the function = tr(AB) defines an inner product on Mn?
1-Find the cosine of the angle between A and B with respect to the standard inner product on M22 2 4 A = (-²₁₂3) B = (-3² ₂) 1 4 2 2-Let A, B E M .Determine whether if the function = tr(AB) defines an inner product on Mn?
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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Do q2 only plz
![1. Find the cosine of the angle between \( A \) and \( B \) with respect to the standard inner product on \( M_{22} \).
\[
A = \begin{pmatrix} 2 & 4 \\ -1 & 3 \end{pmatrix} \quad B = \begin{pmatrix} -3 & 1 \\ 4 & 2 \end{pmatrix}
\]
2. Let \( A, B \in M_{nn} \). Determine whether the function
\[
\langle A, B \rangle = \text{tr}(AB)
\]
defines an inner product on \( M_{nn} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b2b9d69-854a-4c26-a639-4c378ed4e00f%2Fa51f5590-3de3-495f-a914-0a28cd03cb33%2Ff18q47r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Find the cosine of the angle between \( A \) and \( B \) with respect to the standard inner product on \( M_{22} \).
\[
A = \begin{pmatrix} 2 & 4 \\ -1 & 3 \end{pmatrix} \quad B = \begin{pmatrix} -3 & 1 \\ 4 & 2 \end{pmatrix}
\]
2. Let \( A, B \in M_{nn} \). Determine whether the function
\[
\langle A, B \rangle = \text{tr}(AB)
\]
defines an inner product on \( M_{nn} \).
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