Find the dimensions of the null space and the column space of the given matrix. A...
2. * Let A be an m xn matrix, let Col(A) be the column space of A, and let Nul(A) be the null space of A. (a) Show that Nul(A) is a subspace of R". (b) Show that Col(A) is a subspace of RM
If the null space of a 7 x8 matrix is 2-dimensional, find rank A, dim RowA, and dim Col A OA rank A-5, dim Row A 5, dim Col A 5 OB. rank A 6, dim Row A-6, dim Col A 2 OC. rank A-6, dim Row A-6, dim Col A-6 OD. rank A 6, dim Row A 2, dim Col A-2
1. For the matrix A given below, find col(A) and Nul(A). Also determine if the given vector is in the column space, null space, both or neither. A = -2 -5 1 3 3 11 1 7 8 -5 -19 -13 0 1 7 5 -171 5 1 -3 1 5 1
Question 4 2 pts Determine whether the vector u is in the column space of the matrix A and whether it is the null space of A. 1 0 3 1 -2 1 - 4 U = 3 3 0 4 - 1 3 6 Not in Col A in Nul A In Col A, not in Nul A Not in ColA, not in Nul A In Col A and in Nul A Question 5 1 pts 1 co 2...
If the null space of a 6x 12 matrix A is 6-dimensional, what is the dimension of the column space of A? dim Col A= (Simplify your answer.)
1) Find the rank of A 2) Find the dimensions of Nul(A) and Col(A) 3) How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A ? 9 3 2 27 18 A 6 9 2 2 Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(.A). (3). How do the dimensions of Nul(A) and Col(A)...
(1 point) Find a basis for the column space, row space and null space of the matrix 8 -4 4 -2 6 2 -5 -4 1 -1 -3 2 -1 Basis of column space: {T Basis of row space: OTT {{ Basis of row space: Basis of null space:
22. (a) Find two vectors that span the null space of A 3 -1 2 -4 (b) Use the result of part (a) to find the matrix that projects vectors onto the null space of A. (c) Find two orthogonal vectors that span the null space of A. (d) Use the result of (c) to find the matrix that projects vectors onto the nul space of A. Compare this matrix with the one found in part (a). (e) Find the...
1 1. The matrix A and it reduced echelon form B are given below. 1 -2 9 5 4 1 0 3 0 0 -1 6 5 -3 0 1 -3 0 -7 A= ~B= -2 0 -6 1 -2 0 0 1 -2 4 9 1 -9 0 0 0 0 0 (a) Find p, q, r s.t Nul A, Col A, Row A is a subspace of RP, R9, R”, respectively o 1 Answer. p = a =...
For an n x m matrix B, the sum of the dimensions of the column space and the null space equals m. True False