Homework Help is Here – Start Your Trial Now!
Math
Algebra
(A8)", (^)*, * (21)*". Use the inverse matrices to find and 1 3 1 4 2. 4 2 A-1 = 1 1 B-1 2 4 2 4 3 1 -2 2 2 4 4 2. -1 АВ (a) (b) -1 (e) (24)

(A8)", (^)*, * (21)*". Use the inverse matrices to find and 1 3 1 4 2. 4 2 A-1 = 1 1 B-1 2 4 2 4 3 1 -2 2 2 4 4 2. -1 АВ (a) (b) -1 (e) (24)

Algebra and Trigonometry (6th Edition)
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,...
See similar textbooks
icon
Related questions
Question

2.3

7.

pls help

**Use the inverse matrices to find \( (AB)^{-1} \), \( (A^T)^{-1} \), and \( (2A)^{-1} \).** Given: \[ A^{-1} = \begin{bmatrix} \frac{1}{2} & 1 & \frac{3}{4} \\ 1 & -2 & \frac{1}{4} \\ -2 & 1 & \frac{1}{2} \end{bmatrix}, \quad B^{-1} = \begin{bmatrix} 2 & 1 & 4 \\ 2 & \frac{1}{2} & 2 \\ 1 & -\frac{3}{4} & 2 \end{bmatrix} \] **(a) \( (AB)^{-1} \)** Diagram with three rows and three columns of empty boxes indicating the positions for each element of the resulting inverse matrix. There are green arrows pointing right and downward, implying the order and direction for filling in the matrix. **(b) \( (A^T)^{-1} \)** Another similar diagram with empty boxes structured in a 3x3 matrix format, with green arrows indicating the direction for determining the elements of the inverse of the transpose of matrix \( A \). **(c) \( (2A)^{-1} \)** The third diagram, following the same format. It shows empty boxes for a 3x3 matrix, with green arrows pointing right and downward to help guide solving for the inverse of \( 2A \). In each sub-section, students are expected to compute the inverse matrices based on the provided inverse matrices of \( A \) and \( B \), applying the necessary mathematical rules and operations for matrix inverses.
Transcribed Image Text:**Use the inverse matrices to find \( (AB)^{-1} \), \( (A^T)^{-1} \), and \( (2A)^{-1} \).** Given: \[ A^{-1} = \begin{bmatrix} \frac{1}{2} & 1 & \frac{3}{4} \\ 1 & -2 & \frac{1}{4} \\ -2 & 1 & \frac{1}{2} \end{bmatrix}, \quad B^{-1} = \begin{bmatrix} 2 & 1 & 4 \\ 2 & \frac{1}{2} & 2 \\ 1 & -\frac{3}{4} & 2 \end{bmatrix} \] **(a) \( (AB)^{-1} \)** Diagram with three rows and three columns of empty boxes indicating the positions for each element of the resulting inverse matrix. There are green arrows pointing right and downward, implying the order and direction for filling in the matrix. **(b) \( (A^T)^{-1} \)** Another similar diagram with empty boxes structured in a 3x3 matrix format, with green arrows indicating the direction for determining the elements of the inverse of the transpose of matrix \( A \). **(c) \( (2A)^{-1} \)** The third diagram, following the same format. It shows empty boxes for a 3x3 matrix, with green arrows pointing right and downward to help guide solving for the inverse of \( 2A \). In each sub-section, students are expected to compute the inverse matrices based on the provided inverse matrices of \( A \) and \( B \), applying the necessary mathematical rules and operations for matrix inverses.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS