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Vijay posted an Question
October 02, 2022 • 02:01 am 30 points
  • CSIR NET
  • Mathematical Sciences

|let a be a 4x4 matrix such that -1,1,1, -2 are its eigenvalues. if b = a* - 5a* +51, then trace (a + b) equals

|Let A be a 4x4 matrix such that -1,1,1, -2 are its eigenvalues. If B = A* - 5A* +51, then trace (A + B) equals

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  • Dr. avtar chand Best Answer

    eigen value of A -1,1,1,-2 eigen value of A² 1,1,1,4 eigen value of A⁴ 1,1,1,16 tr(A)=-1 B=A⁴-5A²+5I (A+B)=A⁴-5A²+A+5I tr(A+B)=tr(A⁴)-5tr(A²)+tr(A)+5tr(I) =19-35-1+15=-2

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