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`if A=[{:(1,-1,1),(2,1,-1),(-1,-2,2):}]` then show that `A^(-1)` Does not exist. |
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Answer» We have `[{:(1,-1," "1),(2," "1,-1),(-1,-2," "2):}]=[{:(1,0,0),(0,1,0),(0,0,1):}].A` `implies" "[{:(1,-1," "1),(0," "3,-3),(0,-3," "3):}]=[{:(1,0,0),(-2,1,0),(1,0,1):}].A" "[{:(R_(2)toR_(2)-2R_(1)),(R_(3)toR_(3)+R_(1)):}]` `implies" "[{:(1,-1," "1),(0," "3,-3),(0," "0," "0):}]=[{:(1,0,0),(-2,1,0),(-1,1,1):}].A" "[R_(3)toR_(3)+R_(2)].` Thus, we have all zeros in 3rd row of the left-hand side matrix. Hence, `A^(-1)` does not exist. |
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