1 2 -1 0 0 1 0 0 -1 3 ſi 2 0 2 5 [10 (11 points) The matrix A= 2 1 3 2 7 reduces to R= 0 3 1 a 6 5 0 1 Let ui, , 13, 144, and us be the columns of U. (a) Determine, with justification, whether each of the following sets is linearly independent or linearly dependent. i. {u1, 12, 13) ii. {u1, 13, us} iii. {u2, 13} iv. {u1, 12, 13,...
(33 pts) This question is about the matrix = ſi 2 [3 2 0 4 1 6 3 1] 4 9 co (a) Find a lower triangular L and an upper triangular U so that A = LU. (b) Find the reduced row echelon form R = rref(A). How many independent columns in A? (c) If the vector b is the sum of the four columns of A, write down the complete solution to Ax = b
Question 3) (8 points) Consider the following matrix: A= ſi 4 0 0 28 3 12 2 11 -5 5 6 0 8 1 (a) Find a basis for the Rowspace(A). Then state the dimension of the Rowspace(A). (b) Find a basis for the Colspace(A). Then state the dimension of the Colspace(A). (e) Find a basis for the Nullspace(A). Then state the dimension of the Nullspace(A). (d) State and confirm the Rank-Nullity Theorem for this matrix.
Question 3
please answer clearly.
A matrix A and its reduced row echelon form are given as follows: [ 2 1 3 41 | 1 2 0 2 A= 3 21 12 | 3 -1 7 9 18 7 9 -4 and rref(A) = [ 1 0 201 0 1 -1 0 0 0 0 1 0 0 0 0 | 0 0 0 0 Use this information to answer the following questions. (a) Is the column vector u= in...
For the following questions, consider the matrix: ſi 0 21 0 1 0 A= 1 -1 2 0 1 0 1 Please circle the correct answer in parts (a.)-(e.). (a.) The rank of A is 1 2 3 4 (b.) Any basis for the range space of A, R(A), will consist of how many vectors? 1 2 3 4 (c.) The dimension of the null space of A, dim(N(A)) is: 0 1 2 3 (d.) The following vector is in...
1 3 -2 -5 2 11 1. Let A= 3 9 -5 -13 6 3 1 -2 -6 8 18 -1 -1 (a) Find a basis for the row space of A, i.e. Row(A). (b) Find a basis for the column space of A, i.e. Col(A). (c) Find a basis for the null space of A, i.e. Null(A). (d) Determine rankA and dim(Null(A)).
2 3 12 3 37 1. Let A - 10 15 40 7 1131 2 3 7 2 2 and B 1-2 -3 8 3 171 echelon form of A. (Assume this!) (a) (2 pt) What is the value of rank(A)? 110057 100 100 000121The B is the reduced to loooool (b) (2 pt) What is the value of nullity(AT)? (Read carefully (C) (3 pt) Find a basis for col(A). Circle your final answer. (d) (3 pt) Find a basis...
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...
[1 -1 0 0 -2 0] 1 4 -4 0 0 -8 0 (1 point) Let A = 10 0 -1 2 -3 3 . Find a basis for the row space of A, a basis for the column space of A, a basis for the null space 0 0 0 -3 0 -2 Lo 0 1 0 3 3] [1 -1 0 0 -2 01 0 0 1 0 3 0 of A, the rank of A, and the...
Please answer from part a through u
The Fundamental Matrix Spaces: Consider the augmented matrix: 2 -3 -4 -9 -4 -5 6 7 6 -8 4 1 3 -2 -2 9 -5 -11 -17 -16 3 -2 -2 7 14 -7 2 7 8 12 [A[/] = 2 6 | -2 -4 -9 | -3 -3 -1 | -10 8 11 | 11 1 8 / 7 -10 31 -17 with rref R= [100 5 6 0 3 | 4...