Given the basis V₁ = (1,-1,0), V2 = (2, 1, 0), V3 = (0,1,1) use the Gram-Schmidt algorithm to construct an ONB.

Find a 3 x 3 matrix A (with real number entries) whose characteristic polynomial is det(A – zls): * + 2 + 3r +9. A =

Illustrate ALGORITHM Chains of Generalized Eigenvectors?

Make 2 multipart questions with 3 parts using the any of the following topics of "Matrix Operations, Subspaces, Subspaces Assosiated with Matricies, Basis, Dimension and rank, Introduction to Linear Transformation, Markov Chains, Complex Numbers". Make sure to explain in each part how the question would be benefical to a student answering the question.