Question 2 (2 points) a mapping induced by the matrix 2] A = [1 0 lo...
1. Find the induced 2-norm, induced oo-norm, and Frobenius norm of the matrix below. A /0 (-3 1)
True or False? The matrix A = {{1, 0, 0, 0, 0},{2, -2, 0, 0,
0},{-1, 0, 3, 0, 0}{6, -9, 4, 2, 0},{7, 3, -2, 8, 5}} is
diagonalizable.
Question 5. (a) Diagonalize the matrix S = [1 0 -11 -1 2-1 and calculate A100. 1-2 0 0 (b) Diagonalize the matrix A and find a matrix B so that B2 = A. (2 007 (c) Show that the matrix H = 3 2 0 is not diagonalizable. How many linearly independent eigen- LO O 3] vectors does H have?
3 2 0 3. Compute the product 0 01-1 0 013 4. If the matrix A from the previous problem represents a linear transformation T, determine: (a.) Is the mapping onto (b.) Is the mapping one to one (c.) Is the mapping homomorphic (d.) Is the mapping isomorphic (e.) What is the range space? The rank? (f) What is the null space? The nullity? (g.) Does this transformation preserve magnitude? 5. (a.) What is AT, the transpose of the matrix...
(1 point) The matrix [-1 0 -2] A = | 2 -3 -2 lo 0 -3] has two real eigenvalues, l1 = -3 of multiplicity 2, and 12 = -1 of multiplicity 1. Find an orthonormal basis for the eigenspace corresponding to 11.
5 points 1. True of False: a. if A is an n x1 matrix and B is a 1 xn matrix, then AB is an n xn matrix. b. if A is an n x1 matrix and B is a 1 x n matrix, then BA is not defined. 20 points 2. Use the Invertible Matrix Theorem to determine which of the matrices below are invert- ible. Use as few calculations as possible. Justify your answers. [34 01 4 5...
The nullity of the matrix 1 -2 0 3-4 3 2 81 4 A= -1 2 0 4-3 1 5 7 6 0 is n (A) = 3. True False
1) a) If A is a 4×5 matrix and B is a 5×2 matrix, then size of AB is: b) If C is a 3×4 matrix and size of DC is 2×4 matrix , then size of D is: c) True or False: If A and B are both 3 × 3 then AB = BA d) The 2 × 2 identity matrix is: I = e) Shade the region 3x + 2y > 6. f) Write the augmented matrix...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6 -2 1 a. (4 pts) Find the multipliers l21, 131,132 and the elemention matrices E21, E31, E32 b. (2 pts) Use the multipliers l21, 131,132 to construct the lower triangular matrix, L c. (2 pts) Use the elimination matrices to determine the upper triangular, U, matrix of A d. (2 pts) verify that LU A