At what value of ray matrix [A B C D] is the ray unaffected by it?
4. Two lenses /¡ and f2 are separated by a distance d. a) Evaluate the ray transfer matrix that describes the optical system. b) What is the effective focal length of the optical system when d-fi +2? c) When d-fi+f2, what is the angular magnification of the system? d) Under what circumstances is the image of an object at infinity inverted? e) What optical instrument is this?
4. Two lenses /¡ and f2 are separated by a distance d. a)...
Below is a correlation matrix for four variables (labeled A, B, C, and D). which value in the matrix indicates the strongest relationship? A B C B .64 C -.59 .45 D -.65 .52 -.27 Select one -.65 .64 -.59 .52
3. (10 points) Show that the determinant of a matrix is unaffected by a unitary change of basis, i.e. show det det (Ut2U)
For what values of a, b, c and d the following matrix equation
is met:
a=__________ ; b= ________ ; c=_________ and d=_________
(1 C02 (1c0 19 15 -3 a-3 1 -3 a -3 1 = 40 40 0 bd 6) bd 6) 13 - 15 19
Consider the data matrix
(A) Center the data. (B) Find the SVD for the centered A. (C) Compute A', obtained by replacing the smallest singular value in Σ by 0. ' (D) What percentage of the total variance of A is preserved by A'? 3 21 A= 1 0-2
(A) Center the data. (B) Find the SVD for the centered A. (C) Compute A', obtained by replacing the smallest singular value in Σ by 0. ' (D) What percentage of...
Solve the following matrix equation for a, b, c, and d. [a- b+c ] [ 12 1] 3d + 2a-4d10 8 d =
: (a) For what values of a, b, and c is the following matrix symmetric? [-3 5a-c I a 2 La +95 c 5a +267 8 . (b) An nxn matrix A is called skew-symmetric if A= -A. What values of a, b, c, and d now make th following matrix skew-symmetric? ſd Sa-c 5a + 267 08-4d C 0 La +95
Consider a 2x2 transition matrix P consisting of column vectors [a c] and [b d]. The matrix P has two eigenvalues: 1 and k. Find the value of k in terms of the elements of the matrix P and place constraints of the values of k. Calculate eigenvectors for each eigenvalue and hence write down the matrix S whose columns are the eigenvalues of P.
What is shown in the following X-Ray? Select one: a. Lung cancer b. Bronchitis C. Tuberculosis d. Pleurisy e. Community acquired pneumonia
D.30. For the matrix a. Find the eigenvalue(s) and the eigenvector(s). b. Is matrix A diagonalizable? If so, what is the matrix P that diagonalizes A? c. If matrix A is diagonalizable, find the diagonal matrix D that is associated with A by using D-P AP d. If matrix A is diagonalizable, find the diagonal matrix D that is associated with A directly from the eigenvalues found in part a.