If the null space of a 7 x8 matrix is 2-dimensional, find rank A, dim RowA,...
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.)
Find the dimensions of the null space and the column space of the given matrix. A = al 3-4 3 -2 -4 -3 -4 dim Nul A = 3, dim Col A = 2 dim Nul A = 3, dim Col A = 3 dim Nul A = 2, dim Col A = 3 dim Nul A = 4, dim Col A = 1
4. If A is a 7x5 matrix with rank 3, then it follows that (1) dim (col (A "))= (2)dim (null(A ?))=
Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A, Row A, and Nul A. 1 3 -5 -7 2 1 3 -5 - 7 N -2 -6 12 16 -9 0 0 1 1-5 A= B = 2 6 -16 - 20 34 0 0 0 0 5 -3 -9 6 12 0 0 0 0 0 0 rank A= dim Nul A= A...
Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A Row A and Nul A 1 N A= 2 -5 2 - 2 - 4 - 1 7 -23 -3 -6 -8 17 4 3 6 10 - 19 0 B= [122-5 2 0 0 1 -1 -5 000 0 - 4 000 0 0 rank A= dim Nul A A basis for Col Ais...
Find a basis for the row space and the rank of the matrix. -3 -6 6 5 4 -4 -4 2 -3 -6 6 9 (a) a basis for the row space 33} (b) the rank of the matrix 3
(a) Why is it impossible for a 3 x 4 matrix A to have rank 4 and dim Nul A = 0? (b) What is the rank of a 6 x 8 matrix whose null space is three-dimensional? (c) If possible, construct a 3 x 5 matrix B such that dim Nul B =3 and rank B = 2. Explain your reasoning. (d) Construct a 4 x 3 matrix C with rank 1. It need not be complicated.
Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A, Row A, and Nul A. 1 2-2 4-5 1 2-2 -4 -5 00 1 -4 0 0 0 05 3 6 -814-12 -3 -6 14 20 0 rank A 3 dim Nul A= 2 2 812 A basis for Col A is 2 -314 (Use a comma to separate vectors as needed.) 2 A basis...
Please be as detailed as possible. Find a basis for the row space and the rank of the matrix. r-2-8 8 5 З 12-12-4 -2 -8 89 (a) a basis for the row space [1,4,-4,0;0,0,0,1 (b) the rank of the matrix No Response)2 Find a basis for the row space and the rank of the matrix. r-2-8 8 5 З 12-12-4 -2 -8 89 (a) a basis for the row space [1,4,-4,0;0,0,0,1 (b) the rank of the matrix No Response)2
Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space and rank of AT respectively are 1,3,1 1, 1,3 3,1,1 1,3,3