Question

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 _________.
A.
B.
C.
D.

Answer 1

Let `M =[[a ,b,c],[d,e,f],[g,h,i]]`
`M= [[0],[1],[0]]= [[-1],[2],[3]]rArr b =-1, e=2. h = 3`
`M [[1],[-1],[0]] = [[1],[1],[-1]] rArr a = 0, d= 3, g= 2`
`M [[1],[1],[1]] = [[0],[0],[12]] rArr g+h+i= 12rArri=7`
`therefore ` Sum of diagonal elements `= a + e + i = 0 + 2+7=9`