Chapter 2 - Linear Systems of Equations and Matrices

Section 2.2 - Augmented Matrix of a Linear System and Row Operations

Example 2.2.1

(A={{5,-3},{2,7}})//MatrixForm

(B={{9},{-4}})//MatrixForm

Join[A,B,2]//MatrixForm

Example 2.2.2

(CM={{6,1,0,4,-3},{-9,2,3,-8,1},{7,0,-4,5,2}})//MatrixForm

(CM1={1/6 CM[[1]],CM[[2]],CM[[3]]})//MatrixForm

(CM2={CM1[[1]],9 CM1[[1]]+CM1[[2]],CM1[[3]]})//MatrixForm

(CM3={CM2[[1]],CM2[[2]],-7 CM2[[1]]+CM2[[3]]})//MatrixForm

(CM4={CM3[[1]],2/7 CM3[[2]],CM3[[3]]})//MatrixForm

(CM5={-1/6 CM4[[2]]+CM4[[1]],CM4[[2]],CM4[[3]]})//MatrixForm

(CM6={CM5[[1]],CM5[[2]],7/6 CM5[[2]]+CM5[[3]]})//MatrixForm

(CM7={CM6[[1]],CM6[[2]],-1/3 CM6[[3]]})//MatrixForm

(CM8={1/7 CM7[[3]]+CM7[[1]],CM7[[2]],CM7[[3]]})//MatrixForm

(CM9={CM8[[1]],-6/7 CM8[[3]]+CM8[[2]],CM8[[3]]})//MatrixForm

Solve[{6 x+y+4 w==-3,-9 x+2 y+3 z-8 w==1,7 x-4 z+5 w==2},{x,y,z}]

Example 2.2.3

(B={{2,-3 I,-4,-1+2 I},{2-2 I,3,1-I,-2 I},{10-4 I,6-9 I,-10-2 I,-3+2 I}})//MatrixForm

(B1={1/2 B[[1]],B[[2]],B[[3]]})//MatrixForm

(B2={B1[[1]],(2 I-2) B1[[1]]+B1[[2]],(4 I-10) B1[[1]]+B1[[3]]})//MatrixForm

(B3={B2[[1]],1/(6+3 I) B2[[2]],B2[[3]]})//MatrixForm

(B4={3/2 I B3[[2]]+B3[[1]],B3[[2]],-(6 I+12) B3[[2]]+B3[[3]]})//MatrixForm

Solve[{2 x-3 I y-4 z==-1+2 I,(2-2 I) x+3 y+(1-I) z==-2 I,(10-4 I) x+(6-9 I) y+(-10-2 I) z==-3+2 I},{x,y}]

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