Problem 2 Find an orthonormal basis for span 1 3 D
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- question 11 Prove that similar matrices have the same characteristic polynomial. plz provide handwritten mathmatical proveGiven the following Matrix: A = 2 2 2 2 0 0 2 0 0 a) ) Find an orthonormal basis for R3 consisting of eigenvectors of A. b) Find an orthogonal matrix Q and a diagonal matrix D so that QTAQ = D. (attached is work so far finding the characteristic polynomial p(λ) of A, and the eigenvalues of A)Question 2.b. Show that if char(x) has distinct roots, then there exists a basis v1....vn with repsect to which the matrix for L is diagonal.
- Question 16: Classify the definiteness of the quadratic form associtated to the given matrix:The matrix A= [1 −3] [1 k] has two distinct real eigenvalues if and only if k>?Given the following matrix: A = 1 1 1 1 1 1 1 1 1 How can you find a basis for the eigenspace corresponding to λ = 0, when you know that λ = 0 is an eigenvalue of A?
- Please written by computer source Question 2 If vec (w) is an eigenvector of A, how does the vector Avec (w) compare geometrically to the vector vec (w) ?Given the following Matrix: A = 2 2 2 2 0 0 2 0 0 a) ) Find an orthonormal basis for R3 consisting of eigenvectors of A. b) Find an orthogonal matrix Q and a diagonal matrix D so that QTAQ = D. (attached is work finding the characteristic polynomial p(λ) of A, and the eigenvalues of A in the order of λ1 ≥ λ2 ≥ λ3.)Find the roots and characteristic vectors (Values and Eigenvectors) of Matrices A and B as follows : (in the picture)
- Given vectors {|0>, |1>} in the basis of 2x2 matrix: 1 0 0 -1 with eigenvalues +1 and -1 respectively, what are |0> and |1> explictly?Is λ=4 an eigen value of [ 3 0 −12 3 1−3 4 5 ] ? If so, find one corresponding eigen vector?Need help with PDE finding eigenvalues and eigenfunctions of the given Sturm-Liouville Problems