2) (8 points) Consider the matrix A=10 1-1-2 » Find the full set of solutions to Ai-1 0 What is the rank of A, give a basis of its column space and its row space. What is the dimension of its Nullspace and its left Nullspace? (you do not need to compute these subspaces) .Find a basis of its left nullspace (hint: you may need to compute RREF(AT). 2) (8 points) Consider the matrix A=10 1-1-2 » Find the full...
Find bases for the four fundamental subspaces of the matrix A as follows. N(A) = nullspace of A N(AT) = nullspace of AT R(A) = column space of A R(AT) = column space of AT Then show that N(A) = R(A) and N(AT) = R(A)". 1 1 0 0 2-3 -1 1-3 N(A) = 11 N(AT) 11 R(A) 11 R(A) = 3 1
Find bases for the four fundamental subspaces of the matrix A as follows. N(A) = nullspace of A NCA") = nullspace of A? = column space of A R(AT) = column space of AT Then show that N(A) = R(AT) and N(AT) = R(A) 1 1 21 02 3 -1-3-5 NCA) NCA) = R(A) R(A)
[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without multiplying the matrices, 0 -1 1110 0 0 0 (a) Find the dimension of each of the four fundamental subspaces. b have a solution? (b) For what column vector b (b, b2, ba)' does the system AX (c) Find a basis for N(A) and for N(AT). [1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without...
Find bases for the four fundamental subspaces of the matrix A. 1 0 0 A= 0 1 1 1 1 1 1 8 8 N(A)-basis 11 N(AT)-basis R(A)-basis R(AT)-basis
Find bases for the four fundamental subspaces of the matrix A 1 4 9 0 20 N(A)-basis NCAT) = R(A)-basis R (A' )-basis
Find bases for the four fundamental subspaces of the matrix A. 1 0 0 Аа 0 1 1 1 1 1 8 8 N(A)-basis 11 N(AT)-basis R(A)-basis 11 R(AT)-basis { 11
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...
0 1 1 0 0 0 2 0 0 3. (8) Given A 0 0 0 0 0 Find: (1) an orthonormal basis for each of the fundamental subspaces of A; (2) the pseudo-inverse of A; (3) the projection matrix of the column space and the projection matrix of the row space of A.
-15 Find bases for the four fundamental subspaces of the matrix A. 1 8 1 A= 0 60 N(A)-basis If N(AT)= R(A)-basis H KT R(AT)-basis Need Help? Read It Talk to a Tutor