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)?
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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):
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.
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