Let `M` be a `3xx3` matrix satisfying `M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1 1]=[0 0 12]` Then the sum of the diagonal entries of `M` is _________.

Answer

9

Explanation

`M[{:(0,1,1),(1,-1,1),(0,0,1):}]=[{:(-1,1,0),(2,1,0),(3,-1,12):}]`
At `A=[{:(0,1,1),(1,-1,0),(0,0,1):}],B=[{:(-1,1,0),(2,1,0),(3,-1,12):}]`
`impliesMA=BimpliesM=BA^(-1)`
`impliesM=[{:(-1,1,1),(2,1,0),(3,-1,12):}][{:(1,1,-2),(1,0,-1),(0,0,1):}]`
`(A^(-1)=[{:(1,1,-2),(1,0,-1),(0,0,1):}])`
`impliesM=[{:(0,-1,1),(3,2,-5),(2,3,7):}]`
Sum of diagonal elements `0+2+7=9`