Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Title:** Comparing Inverse Matrices
**Objective:** Compare \((AB)^{-1}\) to \(B^{-1}A^{-1}\) for the given matrices below.
**Matrices:**
\( A = \begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 9 \\ 1 & 2 \end{bmatrix} \)
---
**Calculation:**
1. **Find \((AB)^{-1}\):**
\[
(AB)^{-1} = \begin{bmatrix} \text{[Input matrix elements as integers or simplified fractions]} \end{bmatrix}
\]
2. **Find \(B^{-1}A^{-1}\):**
\[
B^{-1}A^{-1} = \begin{bmatrix} \text{[Input matrix elements as integers or simplified fractions]} \end{bmatrix}
\]
**Conclusion:**
Determine which of the following is true:
- **A.** \((AB)^{-1} = A^{-1}B^{-1}\)
- **B.** \((AB)^{-1} = B^{-1}A^{-1}\)
- **C.** \((AB)^{-1} = AB^{-1}\)
- **D.** \((AB)^{-1} \neq B^{-1}A^{-1}\)
**Instructions:**
- Type an integer or a simplified fraction for each matrix element.
- Review your calculations and choose the correct conclusion based on your results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda71f516-efb8-4c35-a511-98b13aff5a74%2F54b7ee27-8d89-4b15-acf7-77582405fde7%2Flvs1r38_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title:** Comparing Inverse Matrices
**Objective:** Compare \((AB)^{-1}\) to \(B^{-1}A^{-1}\) for the given matrices below.
**Matrices:**
\( A = \begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 9 \\ 1 & 2 \end{bmatrix} \)
---
**Calculation:**
1. **Find \((AB)^{-1}\):**
\[
(AB)^{-1} = \begin{bmatrix} \text{[Input matrix elements as integers or simplified fractions]} \end{bmatrix}
\]
2. **Find \(B^{-1}A^{-1}\):**
\[
B^{-1}A^{-1} = \begin{bmatrix} \text{[Input matrix elements as integers or simplified fractions]} \end{bmatrix}
\]
**Conclusion:**
Determine which of the following is true:
- **A.** \((AB)^{-1} = A^{-1}B^{-1}\)
- **B.** \((AB)^{-1} = B^{-1}A^{-1}\)
- **C.** \((AB)^{-1} = AB^{-1}\)
- **D.** \((AB)^{-1} \neq B^{-1}A^{-1}\)
**Instructions:**
- Type an integer or a simplified fraction for each matrix element.
- Review your calculations and choose the correct conclusion based on your results.
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