Question Solved1 Answer 3. Invert these matrices A by the Gauss-Jordan method: [100] (a) Ai = , 1 1 1 0 0 1 2 -1 0 (b) A2: -1 0 -2 -1 -1 2 0T (C) A3 1001 0 1 1 1 1 1

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Transcribed Image Text: 3. Invert these matrices A by the Gauss-Jordan method: [100] (a) Ai = , 1 1 1 0 0 1 2 -1 0 (b) A2: -1 0 -2 -1 -1 2 0T (C) A3 1001 0 1 1 1 1 1
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Transcribed Image Text: 3. Invert these matrices A by the Gauss-Jordan method: [100] (a) Ai = , 1 1 1 0 0 1 2 -1 0 (b) A2: -1 0 -2 -1 -1 2 0T (C) A3 1001 0 1 1 1 1 1
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(c) Given A_(3)=[[0,0,1],[0,1,1],[1,1,1]]|A_(3)|=|[0,0,1],[0,1,1],[1,1,1]|=1(-1)=-1!=0Now we use Gauss. Jordon matrix inversion method{:[[[0,0,1,:,1,0,0],[0,1,1,:,0,1,0],[1,1,1,:,0,0,1]]],[longrightarrow^(R_(1)harrR_(3))[[1,1,1,0,0,0,1],[0,1,1,0,0,1,0],[0,0,1,0,1,0,0]]],[longrightarrow^(R_(1)-R_(2))[[1,0,0,0,0,-1,1],[0,1,1,0,0,1,0],[0,0,1,0,1,0,0]]],[longrightarrow^(R_(2)-R_(3))[[1,0,0,0,-1,1],[0,1,0,i,-1,1,0],[0,0,1,i,1,0,0]]]:}Therefore the inverse of the given matrixA_(3)" is "[[0,-1,1],[-1,1,0],[1,0,0]](3) Given A_(1)=[[1,0,0],[1,1,1],[0,0,1]]Now we use Geauss Jordon's matrix inversion method.{:[[[1,0,0,:,1,0,0],[1,1,1,vdots,0,1,0],[0,0,1,:,0,0,1]]],[longrightarrow^(R_(2)-R_(1))[[1,0,0,0,1,0,0],[0,1,1,vdots,-1,1,0],[0,0,1,0,0,0,1]]],[longrightarrow^(R_(2)-R_(3))[[1,0,0,:,1,0,0],[0,1,0,:,-1,1,-1],[0,0,1,vdots,0,0,1]]]:}Therefore the inverse matrix of the give ... See the full answer