o
1 -1 1 6. Find orthonormal b ases for the four fundamental subsp aces of A...
4. (a) Find a singular value decomposition of A. (b) Based on the decomposition, find the following information of A . rank (A) An orthonormal basis of range(A) An orthonormal basis of null(A) An orthonormal basis of range(A) An orthonormal basis of null(AT) (c) Find an eigendecomposition of A and compare it with the singular value decomposition
4. (a) Find a singular value decomposition of A. (b) Based on the decomposition, find the following information of A . rank (A)...
4. Find the singular value decomposition of matrix 3 6 -3 -6 B 23 -4 17 -16
8. Consider the real matrix As -1 0 (a) (3 pts) Find the singular values of A. (b) (4 pts) Find a singular value decomposition of A. (c) (3 pts) Find
8. Consider the real matrix As -1 0 (a) (3 pts) Find the singular values of A. (b) (4 pts) Find a singular value decomposition of A. (c) (3 pts) Find
3. Answer to the followings (30 points): (a) Find orthonormal vectors u2 93 such that q1, 92 span the column 3/2 space of 2. -2 4. (b) Which of the four fundamental subspace contains 93 (c) What is the least squares solution of Ar= 1,2,7
State the Fundamental Theorem of Linear Algebra for A For each of the following four matrices: Rmxn Identify rank(A); Give bases for both the column space R(A) and the null space N(A); . Determine the full singular value decomposition. For some of these matrices you may be able to determine the SVD "by inspection, without needing any calculations: feel free to take advantage of such opportunities when they exist. (ii)-Bil] (ii) A-li%) ] (iii) A=1 1 1 0 ( i)...
State the Fundamental Theorem of Linear Algebra for A For each of the following four matrices: Rmxn Identify rank(A); Give bases for both the column space R(A) and the null space N(A); . Determine the full singular value decomposition. For some of these matrices you may be able to determine the SVD "by inspection, without needing any calculations: feel free to take advantage of such opportunities when they exist. (ii)-Bil] (ii) A-li%) ] (iii) A=1 1 1 0 ( i)...
1. Find a basis for the four fundamental subspaces of the following matrix
1. Find a basis for the four fundamental subspaces of the following matrix
6. (20") Given the 3 x 3 matrix A- 20 00 (a) compute A'A. (b) find all eigenvalues of AA and their associated eigenwectors (c) write down all singular values of A in descending order (d) find the singular-value decomposition(SVD) A-UEV"
2. Suppose A-1103132 10 9-2 (a) What are the dimensions of the four fundamental subspaces associated with A? (b) Find a basis for each of the four fundamental subspaces. 3. Solve this linear system using an augmented matrix:
2. Suppose A-1103132 10 9-2 (a) What are the dimensions of the four fundamental subspaces associated with A? (b) Find a basis for each of the four fundamental subspaces. 3. Solve this linear system using an augmented matrix:
17. Suppose that 0 00 0 1 1 0 0 0 0 0 2 0 0 0 0 0 0 100 A= 0 0 0 0 0 1 0 0 1 0 0 Find: 1) QH decomposition of A 2) the pseudo-inverse of A 3) an orthonormal basis for each of the four fundamental subspaces of A 4) the projection matrix of the column space and the projection matrix of the row space of A
17. Suppose that 0 00...