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Let M be a 3xx3 matrix satisfying {:M[(0),(1),(0)]=[(1),(-1),(6)]=[(1),(1),(-1)]and","M=[(1),(1),(1)]=[(0),(0),(12)]:} Then the sum of the diagonal entries of M, is

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Solution :Let `M={:[(a,b,C),(X,y,z),(l,m,n)]:}`. Then,
`{:M[(0),(1),(0)]=[(1),(-1),(6)]RARR [(b),(y),(m)]=[(-1),(2),(3)]rArr b=-1,y=2,m=3:}`
`{:M[(1),(-1),(0)]=[(1),(1),(1)]rArr a-b=1,x-y=1,l-m=-1:}`
`rArra=0,x=3,l=2`
and,
`{:M[(1),(1),(1)]=[(0),(0),(12)]rArra+b+c=0,x+y+z=0,l+m+n=12:}`
`rArr c=1,z=-1,n=7`
`:. " Sum of diagonal ELEMENTS of "M=a+y+n=0+2+7=9`


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