4. Calculate the eigenvalues and eigenvectors of the covariance matrix. Arrange the eigenvalues and eigenvectors in descending order as shown: A=[₁2] S= [S₁ $₂] where ₁ and ₂ are the eigenvalues with the corresponding eigenvectors (column vectors) s₁ and s₂, and λ₁ > 1₂. Note: It is recommended for you to retain the actual values. You may use the STORE function of your calculator for easier accessibility. Note that there will be some discrepancies if rounding off will be done during the solution. The principal components are selected to be the eigenvector/s with the highest eigenvalue/s. The number of eigenvectors to be selected varies and depends on various factors. For this problem, we will only select the highest eigenvalue and the corresponding eigenvector will be the principal component. This is also known as the feature vector.

Q: Find cond1(A ) and cond∞(A). State whether th e given matrix is ill-conditioned.

A: The given matrix is A=1-2-36. To Find: cond1(A ) and cond∞(A) for the above matrix. To Check:…

Q: Find the eigenvalues of the matrix a a b c d le a Celect one: P A. Eigenvalues[{{c, a, b}, {a,c, d},…

A:

Q: -3 -1 1 -1 2. 1,

A: Given:  Matrix is given.

Q: 3(4) 5 A = %3D -1 2

A: Here in the given question find the canonical form of the matrix A, which is P-1 A P = B   Find the…

Q: Which matrix has 3 as an eigenvalue? Select one or more: O 6 -6 -4 -9 -6 3 3 3 3. 3. O 1 0 0 0 1 0.…

A: Matrix

Q: eigenvalue eigenvectors of the fONOWing filatrix! a A = 0 b 0 Feel free to assume that a and b are…

A:

Q: 3 find uB. -4 Find the transition matrix P from the basis B = {(3, -1), (1, 1)} of R2 to the basis…

A:

Q: 4. For the 2 x 2 matrix A, indicate which of the following vectors are eigenvectors, and for those…

A: We use the definition of eigenvector to solve the problem

Q: 7. A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What…

A:

Q: {H} Let B = and B' Find the change of base matrix from B' to B and from B to B'

A:

Q: Let A be an n x n matrix over C. An n x n matrix B is called a square root of A if B² = A. Find the…

A:

Q: 5. Let A be an n x n matrix. Show that any collection of eigenvectors of A corresponding to…

A: Let A be a n × n matrix then we have to prove that eigenvectors corresponding to different…

Q: Please consider the following instructions for the next several questions Let M be a 2 x 2 matrix…

A: Let M be a 2×2 matrixLet λ1 ≠ λ2 be eigenvalues of MGiven    m1v1→ = λ1v1→  and mv2→ = λ2v2→Assume…

Q: Let v1 = (1,−1,1),v2 = (2,1,3), and v3 = (−1,−1,2) be eigenvectors of the matrix A corresponding to…

A: We know that a number λ is called an eigenvalue of the matrix A if there is a non-zero vector x such…

Q: Find the eigenvalues and eigenvectors of the given matrix. 100 002 020 The eigenvalue(s) is/are 1,…

A: Given: a matrix, 100002020 To find: Eigenvalues and Eigenvectors of given matrix.

Q: determine how many Jordan canonical forms are possible with the given eigenvalues (not counting…

A: The number of Jordan Canonical forms are possible has to be determined. The given eigenvalues are  λ…

Q: Let e(x) = 1- 4t + 3t² € E₂. Consider the following ordered bases for E B = {1, t, t²} and B' = {t²,…

A: Given : e(x) = 1- 4t +3t2                B  = { 1 , t ,  t2 }     and     B' = {  t2  , t +t2  ,…

Q: (d) Let T be a matrix with only two eigenvalues, 1 and 2. Let u and w be two non-zero eigenvectors…

A: dIt is given that the transformation T be a matrix with only two eigen values1 and 2. Let u and v be…

Q: Find cond1(A ) and cond∞(A). State whether th e given matrix is ill-conditioned.

A: To find:  and

Q: The matrix has eigenvalue X = 2 repeated three times. Find an 2-eigenvector for A: -8 = Give a…

A:

Q: Let 16.5 -3 Find an invertible matrix S and a diagonal matrix D such that S AS= D. S

A:

Q: Let A be a 2x2 matrix with eigenvalues 3 and and corresponding eigenvectors v, = and vz= Let (x) be…

A:

Q: 3 3 11 А %3D 1 3 1 1 1 3 А

A:

Q: Find the eigenvector and eigenvalues of the following 2 x 2 matrix: (!) t

A: As Ax = Yx Here A represents linear transformation  x represents an eigen vector  Here Y means…

Q: Let A E Rx2 be a matrix with (eigenvalue,eigenvectors) = {(2, V1), (–1, 02)}, where Uj = %3D ,and U2…

A:

Q: Consider the given matrix. (: :) Find the eigenvalues. (Enter your answers as a comma-separated…

A: A matrix is a mathematical object containing numbers arranged in rows and columns. If the number of…