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,...
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![**Matrix Inversion Example**
Given the matrix \(A\):
\[ A = \begin{bmatrix} 7 & -8 \\ -8 & -1 \end{bmatrix} ,\]
then,
\[ A^{-1} = \begin{bmatrix} \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \end{bmatrix} .\]
In this example, we are given a 2x2 matrix \(A\) and are asked to find its inverse \(A^{-1}\). To calculate the inverse of a 2x2 matrix:
\[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} ,\]
the inverse is given by:
\[ A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} ,\]
provided that \(ad - bc \neq 0\). This determinant \(ad - bc\) must be non-zero for the inverse to exist.
In the given matrix:
\[ A = \begin{bmatrix} 7 & -8 \\ -8 & -1 \end{bmatrix} ,\]
we would identify \( a = 7, b = -8, c = -8,\) and \(d = -1\) and apply the formula accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e366a85-c23b-450a-9bc7-d2ea0be52d3f%2F75f68af8-35f3-44b8-b26c-f3f8ebfc1fca%2Fpdxp9ut_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix Inversion Example**
Given the matrix \(A\):
\[ A = \begin{bmatrix} 7 & -8 \\ -8 & -1 \end{bmatrix} ,\]
then,
\[ A^{-1} = \begin{bmatrix} \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \end{bmatrix} .\]
In this example, we are given a 2x2 matrix \(A\) and are asked to find its inverse \(A^{-1}\). To calculate the inverse of a 2x2 matrix:
\[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} ,\]
the inverse is given by:
\[ A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} ,\]
provided that \(ad - bc \neq 0\). This determinant \(ad - bc\) must be non-zero for the inverse to exist.
In the given matrix:
\[ A = \begin{bmatrix} 7 & -8 \\ -8 & -1 \end{bmatrix} ,\]
we would identify \( a = 7, b = -8, c = -8,\) and \(d = -1\) and apply the formula accordingly.
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