Question Solved1 Answer Answer Question 6(A2). Make sure its clear to read. Please show all work.  6. Use the Gauss-Jordan method to invert \[ A_{1}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 1 \end{array}\right], \quad A_{2}=\left[\begin{array}{ccc} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{array}\right], \quad A_{3}=\left[\begin{array}{lll} 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right] \]

8RJUJH The Asker · Advanced Mathematics
Answer Question 6(A2). Make sure its clear to read. Please show all work. 
Transcribed Image Text: 6. Use the Gauss-Jordan method to invert \[ A_{1}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 1 \end{array}\right], \quad A_{2}=\left[\begin{array}{ccc} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{array}\right], \quad A_{3}=\left[\begin{array}{lll} 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right] \]
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Transcribed Image Text: 6. Use the Gauss-Jordan method to invert \[ A_{1}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 1 \end{array}\right], \quad A_{2}=\left[\begin{array}{ccc} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{array}\right], \quad A_{3}=\left[\begin{array}{lll} 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right] \]
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Step1/2Solution is given below-Solution :' Gauss Jordan method for Matrix A,{:[[A∣I]],[=>[I∣A^(-1)]]:}where A^(-1) is inverse of A and I is identity matrix Now Given matrix A_(2)=[[2,-1,0],[-1,2,-1],[0,-1,2]]:. By Grauss-Jordan method{:[[A_(2)∣I]=[[2,-1,0,1,0,0],[-1,2,-1,0,1,0],[0,-1,2,0,0,1]]],[" Apply "R_(1)rarrR_(1)+R_(2)],[=[[1,1,-1,1,1,0],[-1,2,-1,0,1,0],[0,-1,2,0,0,1]]],[" Apply "R_(2)longrightarrowR_(2)+R_(3)],[=[[1,1,-1,1,1,0],[-1,1,1,0,1,1],[0,-1,2,0,0,1]]],[" Apply "R_(3)rarrR_(3)+R_(1)],[=[[1,1,-1,1,1,0],[-1,1,1,0,1,1],[1,0,1,1,1,1]]],[" Apply "R_(2)rarrR_(2)+R_(1)],[=[[1,1,-1,1,1,0],[0,2,0,1,2,1],[1,0,1,1,1,1]]]:}Explanation:Please refer to solution in this step.Step2/2Apply R_(1)rarrR_(1)-R=[[2,1,0,2,2,1],[0,2,0,0,1,1],[1,0,1,1,1,1]]Apply R_(1)rarrR_(1)-(1)/(2)R_(2)=[[2,0,0,2,(3)/(2),(1)/(2)],[0,2,0,0,1,1],[1,0,1,1,1,1]]Apply R_(3)rarrR_(3)-(1)/(2)R_(1)=[[2,0,0,2,(3)/(2),(1)/(2)],[0,2,0,0,1,1],[0,0,1,0,(1)/(4),(3)/(4)]]Apply R_(1)rarr(1)/(2)R_(1)and R_(2)rarr(1)/(2)R_(2)=[[1,0,0,1,(3)/(4),(1)/(4)],[0,1,0,0,1//2,1//2],[0,0,1,0,1//4,3//4]]=[[I,∣,A_(2)^(-1)]]A_(2)^(-1)=[[1,3//4,1//4],[0,1//2,1//2],[0,1//4,3//4]]Which is Required matrix for the given matrix A2Explanation:mjx-container[jax="CHTML"] { line-height: 0;}mjx-container [space="1"] { margin-left: .111em;}mjx-container [space="2"] { margin-left: .167em;}mjx-container [space="3"] { margin-left: .222em;}mjx-container [space="4"] { margin-left: .278em;}mjx-container [space="5"] { margin-left: .333em;}mjx-container [rspace="1"] { margin-right: .111em;}mjx-container [rspace="2"] { margin-right: .167em;}mjx-container [rspace="3"] { margin-right: .222em;}mjx-container [rspace="4"] { margin-right: .278em;}mjx-container [rspace="5"] { margin-right: .333em;}mjx-container [size="s"] { font-size: 70.7%;}mjx-container [size="ss"] { font-size: 50%;}mjx-container [size="Tn"] { font-size: 60%;}mjx-container [size="sm"] { font-size: 85%;}mjx-container [size="lg"] { font-size: 120%;}mjx-container [size="Lg"] { font-size: 144%;}mjx-container [size="LG"] { font-size: 173%;}mjx-container [size="hg"] { font-size: 207%;}mjx-container [size="HG"] { font-size: 249%;}mjx-container [width="full"] { width: 100%;}mjx-box { display: inline-block;}mjx-block { display: block;}mjx-itable { display: inline-table;}mjx-row { display: table-row;}mjx-row > * { display: table-cell;}mjx-mtext { display: inline-block; 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