Can anyone please check if i calculated it correctly? #b=diag{1,0,3,5}, p(t)=t^2-1# is #p(b)=diag{0,-1,8,24}#?

can anyone please check if i calculated it correctly? #b=diag{1,0,3,5}, p(t)=t^2-1# is #p(b)=diag{0,-1,8,24}#?

can anyone please check if i calculated it correctly? #b=diag{1,0,3,5}, p(t)=t^2-1# is #p(b)=diag{0,-1,8,24}#?

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SCooke Share
Feb 14, 2018

Answer:

That is correct.

Explanation:

The transformation is of the b{diag} matrix through the p(t) function. Thus, applying the p(t) function to each matrix value derives the p(b) matrix.

#p(t) = t^2 -1# where we substitute b{diag} for t.

#p(1) = 1^2 -1 = 1 - 1 =" " 0#
#p(0) = 0^2 -1 = 0 - 1 =" "-1#
#p(3) = 3^2 -1 = 9 - 1 =" " 8#
#p(5) = 5^2 -1 = 25 - 1 =" " 24#

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