Let A=⎛⎜⎝x2683y2945z2⎞⎟⎠ and B=⎛⎜⎝2x3522y6142z−3⎞⎟⎠ be two matrices and if Tr(A)=Tr(B), then the value of (x+y+z) is equal to (Note: Tr(P) denotes trace of matrix P)
A
0
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B
1
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C
2
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D
3
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Solution
The correct option is C3 tr(A)=x2+y2+z2 tr(B)=2x+2y+2z−3 x2+y2+z2=2x+2y+2z−3 (x−1)2+(y−1)2+(z−1)2=0 x=y=z=1 Hence, (x+y+z)=3