3. Let A = 50 01 2 1 3 2 Onone of these 04 B 3 4 2 3 If A²B³ a b c d then ad - bc =
3. Let A = 50 01 2 1 3 2 Onone of these 04 B 3 4 2 3 If A²B³ a b c d then ad - bc =
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
![**Question 13:**
Let
\[
A = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}
\]
\[
B = \begin{pmatrix} 3 & 4 \\ 2 & 3 \end{pmatrix}
\]
If
\[
A^2B^3 = \begin{pmatrix} a & b \\ c & d \end{pmatrix}
\]
then \( ad - bc = \)
- ☐ 0
- ☐ 1
- ☐ none of these
- ☐ 4
**Explanation:**
This problem involves matrix operations. You are given two matrices, \( A \) and \( B \), and asked to find the determinant of the resulting matrix product \( A^2B^3 \). The determinant of a \( 2 \times 2 \) matrix
\[
\begin{pmatrix} a & b \\ c & d \end{pmatrix}
\]
is calculated as \( ad - bc \).
Choose the correct option based on the determined value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9348d578-66ea-4064-b97e-301aeae52239%2Fe57c1020-f0c7-496e-a6e9-1c54ed95ba9e%2Fzh1qbpd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 13:**
Let
\[
A = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}
\]
\[
B = \begin{pmatrix} 3 & 4 \\ 2 & 3 \end{pmatrix}
\]
If
\[
A^2B^3 = \begin{pmatrix} a & b \\ c & d \end{pmatrix}
\]
then \( ad - bc = \)
- ☐ 0
- ☐ 1
- ☐ none of these
- ☐ 4
**Explanation:**
This problem involves matrix operations. You are given two matrices, \( A \) and \( B \), and asked to find the determinant of the resulting matrix product \( A^2B^3 \). The determinant of a \( 2 \times 2 \) matrix
\[
\begin{pmatrix} a & b \\ c & d \end{pmatrix}
\]
is calculated as \( ad - bc \).
Choose the correct option based on the determined value.
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