Use the matrix P to determine if the matrices A and A' are similar. P=begin{bmatrix}-1 & -1 1& 2 end{bmatrix}, A=begin{bmatrix}14 & 9 -20 & -13 end{bm

Lipossig 2020-10-26 Answered
Use the matrix P to determine if the matrices A and A
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Expert Answer

estenutC
Answered 2020-10-27 Author has 81 answers
Step 1
Given:
P=[1112],A=[1492013] and A=[3222]
If P1AP=A , then the matrices A and A' are similar.
Step 2
First, find P1 as shown below.
P1=1det(P)Adj(P)
=1|1112|[2111]
=12+1[2111]
=(1)[2111]
=[2111]
Step 3
Compute P1AP as follows.
P1AP=[2111][1492013][1112]
=[28+2018+131420913][1112]
=[8564][1112]
=[858106468]
=[3222]
Here, P1AP=A
That implies, the matrices A and A' are similar.
Step 4
Therefore,
P1=[2111] and P1AP=[3222]
And, the correct option is, "Yes, they are similar".
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Jeffrey Jordon
Answered 2022-01-30 Author has 2047 answers

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