Consider the following. A=\([ -5 ,9 ],[-1, 1])/ZSK List

Erik Cantu

Erik Cantu

Answered question

2022-03-27

Consider the following.
A=-59-11
List the eigenvalues of A and bases of the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)
smaller λ-value λ1= ___
smaller λ-value λ2= ___
Find an invertible matrix P and a diagonal matrix D such that p1AP=D. (Enter each matrix in the form row 1row 2, where each row is a comma-separated list. If A is not diagonalizable, enter NO SOLUTION.)
(D,P)=(___)

Answer & Explanation

anghoelv1lw

anghoelv1lw

Beginner2022-03-28Added 19 answers

Step 1
Pms:- Given,Matrix
A=-59-11
To find EigenValues&EigenVectors:-
EigenValues:-
A-dz=0-5-d9-11-d=
(5d)(1d)+9=0
5+5dd+d2+9=0
d2+4d+4=0
(d+2)2=0d=2,2
Step 2
EigemVectors:-
A+2zx=0-39-13n1n2=00
 3x1+9x2=0x1+3x2=0  x1+3x2=0x1  =3x2  
Let x2=1x1=3
V1=31
So,
EigenValue d1=2;Eigenspacespam31
EigenValue d2=2;Eigenspacespam31
Step 3
Since,
The number of EigenVectors is less than dimwnsions of the matrix, then the matrixis not diagonalizable.
Hence,
The matrix is not diagonolizable
Ans:-(B)  No
Since, The matrix is not diagonalizable.So, (D, P) =(No solution)

-3x1+9x2=0-x1+3x2=0-x1+3x2=0x1  =3x2 

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