4. Suppose that AB = AC, where B and C are n x p matrices. Is B = C? What if we also assume that A is invertible?
4. Suppose that AB = AC, where B and C are n x p matrices. Is B = C? What if we also assume that A is invertible?
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
Need question 4
![1. Find the inverse of
\[
\begin{bmatrix}
3 & 2 \\
8 & 5
\end{bmatrix}
\].
2. For what values of \( h \) is
\[
\begin{bmatrix}
1 & h \\
-1 & h
\end{bmatrix}
\]
invertible?
3. Suppose that \( P \) is invertible and that \( A = PBP^{-1} \). Solve for \( B \) in terms of \( A \) and \( P \).
4. Suppose that \( AB = AC \), where \( B \) and \( C \) are \( n \times p \) matrices. Is \( B = C \)? What if we also assume that \( A \) is invertible?
5. Find the inverse of
\[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
1 & 1 & 1 & 0 \\
1 & 1 & 1 & 1
\end{bmatrix}
\].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F327c4acc-aab0-4600-9811-c42079067cf3%2F11449158-a81b-406b-b275-f1c663c47c48%2Fl1zowz6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Find the inverse of
\[
\begin{bmatrix}
3 & 2 \\
8 & 5
\end{bmatrix}
\].
2. For what values of \( h \) is
\[
\begin{bmatrix}
1 & h \\
-1 & h
\end{bmatrix}
\]
invertible?
3. Suppose that \( P \) is invertible and that \( A = PBP^{-1} \). Solve for \( B \) in terms of \( A \) and \( P \).
4. Suppose that \( AB = AC \), where \( B \) and \( C \) are \( n \times p \) matrices. Is \( B = C \)? What if we also assume that \( A \) is invertible?
5. Find the inverse of
\[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
1 & 1 & 1 & 0 \\
1 & 1 & 1 & 1
\end{bmatrix}
\].
Expert Solution
Step 1
Given :
To check : Is and also check the case when A is invertible.
Step by step
Solved in 2 steps
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