5. Given the following matrix 「4202 A 2 1 0 2 2021 (a) Find a basis...
-2 1 2. (12 pts) Given the matrix in a R R-E form: [1 0 0 0 3 0 1 1 0 -2 A 0 0 0 1 [0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(A), and nullity (AT). 1 0 (b) (2 pts) Find a basis for the row space of A. (c) (2 pts) Find a basis for the column space of A. (d) (2 pts) Find a basis for the null space of...
no calculator please 2. (12 pts) Given the matrix in a R R-E form: [1 0 0 0 3 -2 1 1 0 0 0 0 0 1 0 0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(A), and nullity(AT). (b) (2 pts) Find a basis for the row space of A. (c) (2 pts) Find a basis for the column space of A. (d) (2 pts) Find a basis for the null space of A.
2. (12 pts) Given the matrix in a R R-E form: [1 1 0 0 3 0 0 0 1 0 -2 0 A = 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(A), and nullity(AT). (b) (2 pts) Find a basis for the row space of A. (c) (2 pts) Find a basis for the column space of A. (d) (2 pts) Find a...
1 1 Use the fact that matrices A and B are row-equivalent. -2 -5 8 0 -17 3 -51 5 A= -5-9 13 7-67 7-13 5 -3 1 0 1 0 1 0 1 -2 0 B = 3 0 0 0 1-5 0 0 0 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. It (c) Find a basis for the row space of A. lll III...
Use the fact that matrices A and B are row-equivalent. 1 2 1 0 0 2 5 1 1 0 3 7 2 2 -2 5 11 4-1 4 1 0 30-4 0 1 -1 0 BE 2 0 0 0 1 -2 0 0 0 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. III 100- DUL...
Use the fact that matrices A and B are row-equivalent. A = 1 2 1 0 0 2 5 1 1 0 3 7 2 2 -2 10 23 7 -2 10 1 0 3 0-4 0 1 -1 0 2 0 0 0 1 -2 0 0 0 0 0 B = (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c) Find a basis for the row space...
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...
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3 0 7 0 3 5 [51 [51 a) Find a basis for the row space Row(A) of A (b) Find a basis for the column space Col(A) of A (c) Find a basis space d) Find the rank Rank(A) and the nullity of A (e) Determine if the vector v (1,4,-2,5,2) belongs to the null space of A. - As always,[5 is for the...
7. Consider the following matrices 2 3-1 0 1 A=101-2 3 0 0 0-1 2 4 2 3 -1 B-101-2 0 0-1 2 3 -1 0 c=101-2 3 For each matrix, determine (a) The rank. (b) The number of free variables in the solution to the homogeneous system of equa- tions (c) A basis for the column space d) A basis for the null space for matrices A and HB e) Dimension of the column space (f) Nullity (g) Does...
2. Let [8 Marks] 1 2 -1 1 3 -2 a) Find the null space of the matrix A and determine its dimension b) Find the range of the matrix A and determine rank(A) c) State the rank-nullity theorem and verify that it is valid for the matrix A. 2. Let [8 Marks] 1 2 -1 1 3 -2 a) Find the null space of the matrix A and determine its dimension b) Find the range of the matrix A...