(24)*. Use the inverse matrices to find АВ and 1 3 1 4 2. 4 2 1 A-1 = B-1 = 2. 2 2 4 1 -2 2 4 -1 (a) (A8) -13/2 31/4 35/8 |-11/4 39/8 41/16 -45/8 35/8 5/4 (b) (A7) 1/2 -2 1 -1/2 3/2 3/4 1/4 1/2 (24)* (c) 1 2 3/2 2 -1 1/2 |-4 1
(24)*. Use the inverse matrices to find АВ and 1 3 1 4 2. 4 2 1 A-1 = B-1 = 2. 2 2 4 1 -2 2 4 -1 (a) (A8) -13/2 31/4 35/8 |-11/4 39/8 41/16 -45/8 35/8 5/4 (b) (A7) 1/2 -2 1 -1/2 3/2 3/4 1/4 1/2 (24)* (c) 1 2 3/2 2 -1 1/2 |-4 1
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
2.3
7.
pls help
![**Title: Using Inverse Matrices to Solve Problems**
---
**Objective:**
Learn how to find the inverse of matrix expressions: \((AB)^{-1}\), \((A^T)^{-1}\), and \((2A)^{-1}\) using given inverse matrices.
---
**Matrix Definitions:**
- \(A^{-1} = \begin{bmatrix} 1 & 1 & \frac{3}{4} \\ \frac{1}{2} & 2 & 4 \\ 1 & -1 & \frac{1}{2} \\ -2 & 3 & \frac{3}{4} \end{bmatrix}\)
- \(B^{-1} = \begin{bmatrix} 2 & 1 & 2 & 4 \\ 2 & 1 & 2 & 4 \\ \frac{1}{4} & \frac{1}{2} & 3 & 5 \\ \frac{1}{4} & 3 & 4 & 2 \end{bmatrix}\)
---
**Tasks:**
**(a) Finding \((AB)^{-1}\):**
Resulting Matrix:
\[
\begin{bmatrix}
-\frac{13}{2} & \frac{31}{4} & \frac{35}{8} \\
-\frac{11}{4} & \frac{39}{8} & \frac{41}{16} \\
-\frac{45}{8} & \frac{35}{8} & \frac{5}{4}
\end{bmatrix}
\]
**(b) Finding \((A^T)^{-1}\):**
Attempted Matrix (Incorrect):
\[
\begin{bmatrix}
\frac{1}{2} & 1 & -2 \\
1 & -\frac{1}{2} & \frac{3}{2} \\
\frac{3}{4} & \frac{1}{4} & \frac{1}{2}
\end{bmatrix}
\]
**Notes:** A red cross indicates an error in this calculation.
**(c) Finding \((2A)^{-1}\):**
Correct Matrix:
\[
\begin{bmatrix}
1 & 2 & \frac{3}{2} \\
2 & -1 & \frac{1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a7c37e1-d117-46e5-8cc2-cb36983cacd6%2F35013325-d1b5-49a9-b251-a08c66a228ef%2Fw9u6one_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Using Inverse Matrices to Solve Problems**
---
**Objective:**
Learn how to find the inverse of matrix expressions: \((AB)^{-1}\), \((A^T)^{-1}\), and \((2A)^{-1}\) using given inverse matrices.
---
**Matrix Definitions:**
- \(A^{-1} = \begin{bmatrix} 1 & 1 & \frac{3}{4} \\ \frac{1}{2} & 2 & 4 \\ 1 & -1 & \frac{1}{2} \\ -2 & 3 & \frac{3}{4} \end{bmatrix}\)
- \(B^{-1} = \begin{bmatrix} 2 & 1 & 2 & 4 \\ 2 & 1 & 2 & 4 \\ \frac{1}{4} & \frac{1}{2} & 3 & 5 \\ \frac{1}{4} & 3 & 4 & 2 \end{bmatrix}\)
---
**Tasks:**
**(a) Finding \((AB)^{-1}\):**
Resulting Matrix:
\[
\begin{bmatrix}
-\frac{13}{2} & \frac{31}{4} & \frac{35}{8} \\
-\frac{11}{4} & \frac{39}{8} & \frac{41}{16} \\
-\frac{45}{8} & \frac{35}{8} & \frac{5}{4}
\end{bmatrix}
\]
**(b) Finding \((A^T)^{-1}\):**
Attempted Matrix (Incorrect):
\[
\begin{bmatrix}
\frac{1}{2} & 1 & -2 \\
1 & -\frac{1}{2} & \frac{3}{2} \\
\frac{3}{4} & \frac{1}{4} & \frac{1}{2}
\end{bmatrix}
\]
**Notes:** A red cross indicates an error in this calculation.
**(c) Finding \((2A)^{-1}\):**
Correct Matrix:
\[
\begin{bmatrix}
1 & 2 & \frac{3}{2} \\
2 & -1 & \frac{1
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