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4 .   Using   elementary   row   operations ,   find   the   inverse   of   the   following   matrix   : A = 2 - 1 3 - 5 3 1 - 3 2 3

 

Dear Student

Given matrix 2-13-531-323With the augumented matrix2-13-531-323100010001R1R121-1232-531-3231200010001Now  eliminate 1st column by using operationsR2R2+5R1R32R3+3R1  then we get1-1232012172012152120052103201Now perform  R221-1232011701215212005203201Now eliminate second column by performingR1R1+12R2R3R3-12R21010011700-1310520-1-11Now -R31010011700131052011-1Now eliminate 3rd column by performingR1R1-10R3R2R2-17R3100010001-7-910-12-151711-1The inverse of the 2-13-531-323 is  -7-910-12-151711-1

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