

12 3-5 2 U 0 0 0 0 3 (2) A matri A is no1 0 (Thi is not the matris A) (2) A matrix A iownuivalent to This is nohe matrix A! 11 pts] Give the rank and nullity of Λ. rank(A)--null(.)-- 4 pts Does Ar have a solution for every rigt-haud-side ector BYes or No Justify your aswer 2 pts Give a gemetric description for the set all veetrswih the property that A has a solution 4 ptsl...
4 7 5 0 2 2 Problem 7 Let A= -1 2 9 -4 1 5 -1 3 7 3 1 -4 2 0 1 1 0 10 2 a) (4 pts] Using the [V, D] command in MATLAB with rational format, find a diagonal matrix D and a matrix V of maximal rank satisfying the matrix equation A * V = V * D. Is A real-diagonalizable? b) [4 pts) Write down the eigenvalues of A. For each eigenvalue,...
(1) Let X = {0}U[2,3], and give X the topology Tx = {0,{0}, [2, 3], X}. (a) (10 points) Is X To? Briefly justify your answer. (b) (10 points) Is X Hausdorff? Briefly justify your answer. (c) (10 points) Is X Tz? Briefly justify your answer. (d) (10 points) Is D = ({0} Ⓡ {0}) U ([2, 3] x [2, 3]) a closed subset of X x X with the product topology? Briefly justify your answer.
three small problem!!!!!
Problem 7: (9 total points) Let A 11 0 -1 2 1 -1 3 -1 0 = 1 | -2 1 4 -13 3 -1 -5 1 -6 a) Find a basis for ker A. b) Find a 5 x 5 matrix M with rank 2 such that AM = 0, where is the 4 x 5 zero matrix. is the 4 x 5 zero matrix. Prove c) Suppose that B is a 5 x 5 matrix...
(1 point) Let 3 -4 A = -4 -1 -4 -2 -2 If possible, find an invertible matrix P so that D = P-1 AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P= II II D= Be sure you can explain why or why Is A diagonalizable over R? diagonalizable...
(1 point) Let 1-13 153:) -4 -6 6 9 Find a basis for the null space of A. { (1 point) Find the value of k for which the matrix 8 10 -9 A= 4 -4 -9 6 k has rank 2. k=
1. (50 pts.) Let A be the 3 x 3 matrix A= 0 0 3 0 2 0 3 0 0 :) i. Compute the eigenvectors ū1, U2, U3 of A. ii. Verify that the matrix S with columns ū ū2, öz has full rank. iii. Use the Gram-Schmidt process to change B into an orthogonal matrix P.
73126 1. (1 point) Let a and b be real numbers such that a is in the nullspace of [ -1 9 9 0 b What must be the value of a + b? Justify your answer. (CU2OPS08-73128]
1 Problem 7 Let A 4 5 - 1 5 0 2 -1 2 3 -4 7 2 1 3 7 2 -4 2 0 0 10 1 1 a) (4 pts] Using the [V, DJ command in MATLAB with rational format, find a diagonal matrix D and a matrix V of maximal rank satisfying the matrix equation A * V = V * D. Is A real-diagonalizable? b) (4 pts) Write down the eigenvalues of A. For each eigenvalue,...
For each of the unknown matrices below, determine the rank and justify your answer. (a) (1 point) A 3 x 3-matrix whose image is the zero subspace of R. (b) (1 point) A 3 x 2-matrix whose kernel contains the vector (c) (1 point) A 4 x 4-matrix with a 3-eigenspace of dimension 4.