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Question

If the trace of matrix A=sinx0214cosy3sinxsiny3sinz is 8 for x,y,z[0,π], then trace of matrix B=11siny009siny6cosx3sinysinxsinz is

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Solution

Given : Tr(A)=8
sinx4cosy+3sinz=8
which is possible only when
sinx=1,cosy=1 and sinz=1
x=π2,y=π and z=π2 in [0,π]

Now, B=11siny009siny6cosx3sinysinxsinz
Tr(B)=11siny+6cosx+sinz
Tr(B)=00+1
Tr(B)=1

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