4. If A is a 7x5 matrix with rank 3, then it follows that (1) dim...
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
(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...
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
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...
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 10 3 0 0 1 -1 6 5 3 0 1 -3 0 -7 -2 0 -6 1 -2 0 0 0 1 -2 91-9 0 0 0 0 0 (a) Find p, q, rs. Nul A, Col A, Row A is a subspace of R", R9, R', respectively Answer. p = 9=- (b) Find a basis for Nul A (c) Find...
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...
1. Consider the matrix 12 3 4 A 2 3 4 5 3 4 5 6 As a linear transformation, A maps R' to R3. Find a basis for Null(A), the null space of A, and find a basis for Col(A), the column space of A. Describe these spaces geometrically. 2. For A in problem 1, what is Rank(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 1 -2 0 -2 -2 1 1 0 1 -1 0 - 1 1 A= 1 - 1 1 -2 0 -2 -2 2-3 0-3 - 1 0 0 -3 -10 1 - 2 21 5 -2 1 - 1 00 B 1 1 4 3 0 0 00...
4. Yogurt Company makes three yogurt blends: LimeOrange, using 2 quarts of ime yogurt and 2 quarts of orange yogurt per gallon; LimeLemon, using 3 quarts of lime yogurt and 1 quart of lemon yogurt per gallon; and OrangeLemon, using 3 quarts of orange yogurt and 1 quart of lemon yogurt per gallon. Each day the company has 800 quarts of lime yogurt, 650 quarts of orange yogurt, and 350 quarts of lemon yogurt available. 4a. Design a matrix R...