SOLUTION: If v1 = [-5, -5] and v2 = [-5, -2] are eigenvectors of a matrix A corresponding to the eigenvalues λ1=−5 and λ2=4, respectively, then what is A(v1+v2) and A(3v1)?

Question 1160841: If v1 = [-5, -5] and v2 = [-5, -2] are eigenvectors of a matrix A corresponding to the eigenvalues λ1=−5 and λ2=4, respectively, then what is A(v1+v2) and A(3v1)?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.


Under the given condition, A*v1 = the product of the scalar λ1=−5 by the vector v1,

and A*v2 = the product of the scalar λ2= 4 by the vector v2.



Having this hint (instruction), yoy can easily answer the first question.



A(3v1) is the product of the scalar 3λ1= 3*(−5) = -15 by the vector v1.

----------------

You just got comprehensive instructions to complete the assignment on your own.

Do not forget to post your "THANKS" for my help.

RELATED QUESTIONS
if a=(1 1 k 0) the eigenvalues are -4 and 5 find the corresponding... (answered by Edwin McCravy,AnlytcPhil)

if i have a parametric matrix and i want to find parametric Eigenvectors and... (answered by Fombitz)

I have a homework problem that I don't know how to do. I'm asked to solve the following (answered by venugopalramana)

I have been working on trying to find the eigenvalues and eigenvectors of the following... (answered by venugopalramana)

Determine the eigenvalues and the corresponding eligenvectors of the matrix. A=(2 0 1) (answered by ikleyn)

The vector v=[4 5] can be written as a linear combination of the vectors v1=[1 3]... (answered by Edwin McCravy)

This is my second and last question. This is not in a textbook. a.)Let T be a linear... (answered by venugopalramana)

The voltage V1 and V2 are represented as follows V1 = 3sin(wt) V2 = 2cos(wt) If V3 (answered by ikleyn)

Let v1=[2,0,6] , v2=[-1,4,5] , v3=[1,-1,1]. Find the value(s) of k for which b=[2,1,k]... (answered by ikleyn)