Problem 2. TRUE/FALSE. (3 points each) Be sure to clearly state whether the items below are true or false. Then you must fully justify your answer:...
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take home ques 2.png

I get a and b are true But c and d are

also true????

(c) Given vector space V the change of coordinates matrix [Iv]B to B'from B' to B is always diagonalizable

(d) The linear operator T : R^3 -> R^3 that reflects a point (x,y,z) across the plane ax+by+cz=0 (a,b,c element R) is diagonalizable

take home ques 2.png

Problem 2. TRUE/FALSE. (3 points each) Be sure to clearly state whether the items below are
true or false. Then you must fully justify your answer: if true, give a brief explanation (e.g. cite a
relevant theorem from the book or class notes, or show the necessary calculations); if false, supply
a counterexample.
(a) If an n x n matrix A is diagonalizable, then so is A'.
(b) If v is an eigenvector of an n x n matrix A with corresponding eigenvalue ), then v is also an
eigenvector of the matrix A - aln, for every de R.
(c) Given a vector space V, the change of coordinates matrix [Iv] from #' to 8 is always diagonal-
izable.
(d) The linear operator 7 : R3 -> R3 that reflects a point (r, y, z) across
the plane ar + by +c= =0 (a,b,ce R) is diagonalizable.

Top Answer

Yes both c and d are true. For d just... View the full answer

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() Given a vector space v the
change of co-ondinates mattein
From 13 to p is always
diagonalizable.
( True ) Explanation
Let v= R'(R) and B= Ser= (1,010 )
ex = ( 0 , 1,0 )
be the standand bases.
P3...

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