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

Lipossig

Answered question

2020-10-26

Use the matrix P to determine if the matrices A and A

Answer & Explanation

estenutC

estenutC

Skilled2020-10-27Added 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".
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

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