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If A=[{:(1," 2",-1),(3,-2," 5"):}] , th...

If A=`[{:(1," 2",-1),(3,-2," 5"):}]` , then `R_(1) harr R_(2)` and `C_(1) rarr C_(1) + 2C_(3)` given

A

(A) `[{:(-13,2,-5),(-1,2,-1):}]`

B

(B) `[{:(-1,-2,-1),(" 13",-2," 5"):}]`

C

(C) `[{:(" 13",-2," 5"),( -1, " 2", -1):}]`

D

(D) `[{:(2,-13,-5),(2,-1,-1):}]`

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The correct Answer is:
C
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If A=[[1,2,-1],[3,-2,5]],then R_1 harr R_2 and C_1 rarr C_1 + 2C_3 gives

[(1,3,-2),(-3,0,-5),(2,5,0)] =A [(1,0,0),(0,1,0),(0,0,1)] then, C_(2) rarr C_(2)-3C_(1) and C_(3) rarr C_(3) +2C_(1) gives... [(1,0,0),(3,-9,11),(-2,1,4)] =A [(-1,3,2),(0,-1,0),(0,0,-1)] [(1,0,0),(-3,-1,-4),(2,-9,11)] =A [(1,-3,2),(0,1,0),(0,0,1)] [(1,0,0),(-3,1,4),(-2,9,-11)] =A [(-1,3,2),(0,-1,0),(0,0,-1)] [(1,0,0),(-3,9,-11),(2,-1,4)] =A [(1,-3,2),(0,1,0),(0,0,1)]

C_(1) + C_(2) + C_(3) + …… C_(6) = 63

C_(1) + C_(2) + C_(3) + ….. C_(n) = 2^(n)-1

C_(1) + C_(2) + C_(3) + ……….. C_(7) = 127

If A=[(2,-3,3),(2,2,3),(3,-2,2)] then C_(2)+2C_(1) and "then" R_(1)+R_(3) gives