URGENT LINEAR ALGEBRA HELP PLEASE Linear algebra! Alright, so I\'ve got the ques

Question

URGENT LINEAR ALGEBRA HELP PLEASE

Linear algebra! Alright, so I've got the question and I've got the solution for the question but I wanted to know if anyone would be able to explain to me how this is done

The Question is number 24

it approach llC Tnail ldea is to factorA matrix similar to A) in the form A- QiR1, where o? ao and Ri is upper triangular. The factors are interchanged o Ai Ri0i, which is again factored as A 02 R2; then tof Ag = R2Q2, and so on. The similarity of A, A1, … follows from the more general result in Exercise 23. vaiues 0 23. Show that if A QR with Q invertible, then A is simila Al = RQ. 24. Show that if A and B are similar, then det A = det B. .5 3/7 | and Xo = 1 ,5 Note 25. Let A= ,Vi= 4 .7 gen- f the low A is the stochastic matrix studied in Example 5 in Se tion 4.9.] a. Find a basis for R? consisting of vi and another cigenia tor v2 of A.

Explanation / Answer

(24)

Let matrices A and B be similar , then there exists an invertible matrix P such that

B=P^{-1}AP

DetB=Det (P^{-1}AP)

=DetP^{-1}DetADetP

=DetADetP^{-1}DetP

=DetADet(P^{-1}P)

=DetADet(I)

=DetA*1

=Det(A)

Det(B)=Det(A)

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