Consider 01 0 A 1 20 4 (a) Find a basis for Row A and Nul A and hence find the dimension of each....
10 a) Find a basis and the dimension of the row space. b) Find a basis and the dimension of the column space. c) Find a basis and the dimension of the null space. d) Verify the Dimension Theorem for A e) Identify the Domain and Codomain if this is the standard matrix for a linear transformation f) What does the row space represent when this is viewed as a linear transformation? g) Does this represent a linear operator? Explain....
Question 4 (10 marks) t possible to co (a) Col A and Row A; (b) Row A and NulA; (c) Nul A and Col A. Justify the answer for each case with a proof or with an example. Question 4 (10 marks) t possible to co (a) Col A and Row A; (b) Row A and NulA; (c) Nul A and Col A. Justify the answer for each case with a proof or with an example.
please calculate Nul A and dimension of Col A find invertible matrix p and c there are two questions. try and answer them. it is straight forward and clear Determine the dimensions of Nul A and Col A for the matrix shown below. 0 0 A= 1 2 -4 5 -2 6 - 1 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 The dimension of Nul A is and...
basis for the row space of A and its Let A (a) Find dimension 1 1 2 12 o to -S (6) Find a basis for the column Space of A and Its dimensiun (c) Find a bars for the onell space of A and the A @ Find the rank op
(1 point) Let 1 5 -4 |- Find a basis for A -3 Nul(A)'. 0 -1 A basis is {V1, V2} where Vi = V2 II
Question 3 [10 points] Consider the following matrix A and its reduced row-echelon form: A = [-3 3 6 12 0 151 | 1 -1 -2 -4 0 -5 -6 3 9 15 12 18 rret(A) |-1 -1 0 -2 8 -3 [1 0 -1 -1 -4 -1] 01 1 3 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of...
(2 points) Let 4- -1 01 1 1-1 0-2]. Find orthonormal bases of the kernel, row space, and image (column space) of A (b) Basis of the row space: (c) Basis of the image (column space)
4. Consider the matrix [1 0 01 A- 1 0 2-1and the vector b2 (a) Construct the augmented matrix [Alb] and use elementary row operations to trans- form it to reduced row echelon form. (b) Find a basis for the column space of A. (c) Express the vectors v4 and vs, which are column vectors of column 4 and 5 of A, as linear combinations of the vectors in the basis found in (b) (d) Find a basis for the...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of Re"). 2. (12 pts) Given the matrix in a R R-E form: -21 1 [1 0 0 0 3 0 1 1 0 - 2 0 0 0 1 0...
b) fina rank A and basis for col A c) find basis for Nul A Ti 2017 Let A = 2 3 1 1 3 5 1 2 Find the reduced row echelon form of A.