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EP 13.02 . Cline Rows of a Matrix. Consider the ?

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I am struggling with this homework problem. I need help solving problem a, b, and c.

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EP 13.02 . Cline Rows of a Matrix.
Consider the ?* { square matrix`
( a ) [But ] L's Wolfram Alpha (http : / /www . wolframalpha . com/ input / Ti =_ atrix ) to find
the figemnectar representation of It . That is , find A Z* I non - singular matrix U' , it's inverse
matrix LI, and a diagonal matrix !' so that
H = UDU I
[ T ]
State U. I' - and D) . Then prove , by explicit matrix multiplication of your solution for Us, D)
And [ that the right- hand side of the foregoing equation is indeed equal to the left - hand
side , given wur LY, [ ] And !`
( b ) [ 2UP" ] Find a real ?* ?' cube nail matrix , I, of the matrix H . That is, find a matrix {`
such that RE RR*_ And
|} = H .
Then calculate {, by explicit matrix multiplication of your solution for It, in order to prove*
that the left- hand side of my . [ I] is indeed equal to the right- hand side , given your #`
Hint : It may help you to review the solution to HIP S.Of part ( a) first . Then assume that
will can write & in the form A = CALI, where ?' is a diagonal matrix and I' is the non-
singular matrix found in Part (a) . Plug that into the left- hand side ey . [ ?] , to express #` in
tommy al LY, I and I- 1. Also plug cq. [I] for IT into the right- hand side ey. (2). Express !`
in terms of D. Then solve for !, Le, salve for the diagonal matrix elements of !]. keeping
in mind that All matrix elements of It must came out real . Get R from U. C. and L - 1.
( C ) [lop] ( Optional Bonus Problem : Extra Credit! ! Find a compiler ?* I cube root
matrix , R, i.e., another solution of my. [ ?] ahave , such that the eigenvalues of R. donated how
I I and re . both have negative imaginary parts !
Jinfra)* 0 .
Then calculate #`, Wy explicit matrix multiplication of your solution for IT, in order to prove
that the left- hand side of my. [?] is indeed equal to the right- hand side , given Your ``
Hints : For & given non-zero "{ I, the equation " = " has three different complex*
solutions , are EXAM # 1 problem FROLOL part ( a)_ Also can (120^) _ _ _^|{[my = _`
And sin / 120) = sinanaj = * ^

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