(1 point) Find the value of k for which the matrix -8 2 4 A= - 71 -5 -3 3 k has rank 2. k =
(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=
Question 7 [10 points] For the matrix A below, find a value of k so that A has two basic eigenvectors associated with the eigenvalue 1 - -1. A = 293 6 0-1 4k 0 0 -3 -2 0 0 0 -1 k = 0
(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)
9. Find the inverse of the matrix [1 1 k in terms of k Determine all value(s) of k for which the above matrix is not invertible.
True or False? 1. If σ is a singular value of a matrix A, then σ is an eigenvalue of ATA Answer: 2. Every matrix has the same singular values as its transpose Answer: 3. A matrix has a pseudo-inverse if and only if it is not invertible. Answer: 4. If matrix A has rank k, then A has k singular values Answer:_ 5. Every matrix has a singular value decomposit ion Answer:_ 6. Every matrix has a unique singular...
Problem 29: Find a 2-by-3 matrix having rank 1 whose singular value is 2, left singular vector is (1,2)7/V5, and right singular vector is (1,0,1)7/v2. Problem 29: Find a 2-by-3 matrix having rank 1 whose singular value is 2, left singular vector is (1,2)7/V5, and right singular vector is (1,0,1)7/v2.
Question 1 (1 point) Let A be the matrix defined below. -8 8 -8 1 -9 7 4 3 A= 7 6 -7 -9 4 9 5 5 -5 7 6 -7 -1 0 -7 -7 Suppose we know that ele 100 0 1 0 } RREFA= 10 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 Find a basis for the null space of A. O -87 6 5 O -9 9 -9 3...
PLEASE ANSWER ALL PARTS 1. (2 points) For the matrix A=| 3 | 6 | Evaluate (a) A, AA* and AA; (b) the value P (A), where P(x)-x3-1. 2. (1 point) Compute the determinant of the matrix A = | α β 2 -8 6 8 2 -7 7 10 3, (1 point) Compute | 1 -3 0 6 4. (1 point) Find the inverse matrix A-' of the matrix A=1 5 3-2 7 4 -3 5. (3 points) Find...
(1 point) Find k such that the following matrix M is singular. -2 М. 2 -1 3 -1 -3 0 -12 -2 + k k =