Explanation Given: The matrix is A = [ 1 2 3 2 3 4 1 2 1 ] . Theorem used: “Inverse of a square matrix M: If [ M I ] is transformed by row operations into [ I B ] , then the resulting matrix B is M − 1 . However, if we obtain all 0’s in one or more rows to the left of the vertical line, then M − 1 does not exist”. Procedure used: To obtain M − 1 for any n × n matrix M for which M − 1 exists, the below steps are followed. 1. Form the augmented matrix [ M I ] . 2. Perform row operations on [ M I ] to get a matrix of the form [ I B ] where I is the n × n identity matrix. 3. Matrix B is M − 1 . Calculation: Form the augmented matrix [ A I ] in order to obtain the inverse of the matrix. [ 1 2 3 1 0 0 2 3 4 0 1 0 1 2 1 0 0 1 ] Perform row operations on [ A I ] to get the matrix of the form [ I B ] . Obtain 0 for the first entry of the second and third row. [ 1 2 3 1 0 0 0 − 1 − 2 − 2 1 0 0 0 − 2 − 1 0 1 ] ( − 2 ) R 1 + R 2 → R 2 ( − 1 ) R 1 + R 3 → R 3 Multiply the entries of row 2 by –1 and row 3 by − 1 2 . [ 1 2 3 1 0 0 0 1 2 2 − 1 0 0 0 1 1 2 0 − 1 2 ] ( − 1 ) R 2 → R 2 ( − 1 2 ) R 3 → R 3 Make the second entry in row 1 as 0. [ 1 2 0 − 1 2 0 3 2 0 1 0 1 − 1 1 0 0 1 1 2 0 − 1 2 ] ( − 3 ) R 3 + R 1 → R 1 ( − 2 ) R 3 + R 2 → R 2 Make the second entry of the first row as 0. [ 1 0 0 − 5 2 2 − 1 2 0 1 0 1 − 1 1 0 0 1 1 2 0 − 1 2 ] ( − 2 ) R 2 + R 1 → R 1 Thus, after the row operations on the augmented matrix, the matrix of the form [ I B ] is obtained

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134674148

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 4, Problem 25RE

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The inverse A−1 of the given matrix and to show that A−1A=I.

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College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 4.1 - Solve by graphing and check: 2x − y = −3 x + 2y =...Ch. 4.1 - Solve each of the following systems by graphing: x...Ch. 4.1 - Prob. 3MP Ch. 4.1 - Prob. 4MP Ch. 4.1 - Prob. 5MP Ch. 4.1 - Prob. 6MP Ch. 4.1 - Prob. 7MP Ch. 4.1 - Prob. 1ED Ch. 4.1 - Prob. 2ED Ch. 4.1 - In Problems 1–6, find the x and y coordinates of...

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The inverse A − 1 of the given matrix and to show that A − 1 A = I .

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