Question

Find matrix of the inner product with respct to the basis

Answer 1

Answer:

Step-by-step explanation:

(a) B={v1,v2} is a basis of R2 consisting of eigenvectors

We compute that

T(v1)=T([1−1])=[2−2]=2[1−1]=2v1

and

T(v2)=T([11])=[44]=4[11]=4v2.

Thus, v1 is an eigenvector corresponding to the eigenvalue 2 and v2 is an eigenvector corresponding to the eigenvalue 4.

Since v1,v2 are eigenvectors corresponding to distinct eigenvalues, they are linearly independent, and thus B={v1,v2} is a basis of R2.