Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
100%
![The question presented involves finding the inverse of the given matrix \( A \).
Matrix \( A \) is defined as:
\[
A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
\]
The task is to find the inverse \( A^{-1} \). The options provided are:
- **Option A:**
\[
A^{-1} = \begin{bmatrix} -2 & 1 \\ 3 & -\frac{1}{2} \end{bmatrix}
\]
- **Option B:**
\( A^{-1} \) does not exist.
- **Option C:**
\[
A^{-1} = \begin{bmatrix} -1 & -2 \\ -3 & -4 \end{bmatrix}
\]
- **Option D:**
\[
A^{-1} = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}
\]
To select the correct option, students need to understand how to calculate the inverse of a 2x2 matrix using the formula:
\[
A^{-1} = \frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}
\]
where the matrix \( A \) is:
\[
\begin{bmatrix} a & b \\ c & d \end{bmatrix}
\]
For the matrix given: \( a = 1 \), \( b = 2 \), \( c = 3 \), \( d = 4 \). Therefore, students should compute the determinant \( ad-bc \) and then apply the formula to find the correct inverse.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13a2dcc6-42e4-4e14-ac91-024e401b97a3%2Fcc5283fa-9086-4551-9123-90d7f803757a%2Fzjghyq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The question presented involves finding the inverse of the given matrix \( A \).
Matrix \( A \) is defined as:
\[
A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
\]
The task is to find the inverse \( A^{-1} \). The options provided are:
- **Option A:**
\[
A^{-1} = \begin{bmatrix} -2 & 1 \\ 3 & -\frac{1}{2} \end{bmatrix}
\]
- **Option B:**
\( A^{-1} \) does not exist.
- **Option C:**
\[
A^{-1} = \begin{bmatrix} -1 & -2 \\ -3 & -4 \end{bmatrix}
\]
- **Option D:**
\[
A^{-1} = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}
\]
To select the correct option, students need to understand how to calculate the inverse of a 2x2 matrix using the formula:
\[
A^{-1} = \frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}
\]
where the matrix \( A \) is:
\[
\begin{bmatrix} a & b \\ c & d \end{bmatrix}
\]
For the matrix given: \( a = 1 \), \( b = 2 \), \( c = 3 \), \( d = 4 \). Therefore, students should compute the determinant \( ad-bc \) and then apply the formula to find the correct inverse.
Expert Solution
Step p
Find the adjoint of matrix A and divide that with the determinant of matrix A
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education