Matrices In the process todetermine the inverse ofa matrix, you will cometo the following matrixreduction. Completeletters A - I.[1 0 3 JA0 1 6 D E Flo 1 7lG H I]0 3|1B CT1|-1 1 3 o 1 0→-2 1 1lo 001

Given system of matrix is: 103-113-211100010001→103016017ABCDEFGHI By solving this:…

Answered: In the process to determine the inverse…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.3: Inverses Of Matrices And Matrix Equations

Problem 1E

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Question

Matrices

In the process to
determine the inverse of
a matrix, you will come
to the following matrix
reduction. Complete
letters A - I.
[1 0 3 JA
0 1 6 D E F
lo 1 7lG H I]
0 3|1
B CT
1
|-1 1 3 o 1 0→
-2 1 1lo 0
01

Expert Solution

Step 1

Given system of matrix is:

$[\begin{matrix} 1 & 0 & 3 \\ - 1 & 1 & 3 \\ - 2 & 1 & 1 \end{matrix} \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] \to [\begin{matrix} 1 & 0 & 3 \\ 0 & 1 & 6 \\ 0 & 1 & 7 \end{matrix} \begin{matrix} A & B & C \\ D & E & F \\ G & H & I \end{matrix}]$

By solving this:

$[\begin{matrix} 1 & 0 & 3 \\ - 1 & 1 & 3 \\ - 2 & 1 & 1 \end{matrix} \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] R_{2} - (- 1) \cdot R_{1} \to R_{2} [\begin{matrix} 1 & 0 & 3 \\ 0 & 1 & 6 \\ - 2 & 1 & 1 \end{matrix} \begin{matrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

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