matrix is
1 | -3 | 4 | -2 | 5 | 4 |
2 | -6 | 9 | -1 | 8 | 2 |
2 | -6 | 9 | -1 | 9 | 7 |
-1 | 3 | -4 | 2 | -5 | -4 |
convert into Reduced Row Eschelon Form...
Add (-2 * row1) to row2
1 | -3 | 4 | -2 | 5 | 4 |
0 | 0 | 1 | 3 | -2 | -6 |
2 | -6 | 9 | -1 | 9 | 7 |
-1 | 3 | -4 | 2 | -5 | -4 |
Add (-2 * row1) to row3
1 | -3 | 4 | -2 | 5 | 4 |
0 | 0 | 1 | 3 | -2 | -6 |
0 | 0 | 1 | 3 | -1 | -1 |
-1 | 3 | -4 | 2 | -5 | -4 |
Add (1 * row1) to row4
1 | -3 | 4 | -2 | 5 | 4 |
0 | 0 | 1 | 3 | -2 | -6 |
0 | 0 | 1 | 3 | -1 | -1 |
0 | 0 | 0 | 0 | 0 | 0 |
Add (-1 * row2) to row3
1 | -3 | 4 | -2 | 5 | 4 |
0 | 0 | 1 | 3 | -2 | -6 |
0 | 0 | 0 | 0 | 1 | 5 |
0 | 0 | 0 | 0 | 0 | 0 |
Add (2 * row3) to row2
1 | -3 | 4 | -2 | 5 | 4 |
0 | 0 | 1 | 3 | 0 | 4 |
0 | 0 | 0 | 0 | 1 | 5 |
0 | 0 | 0 | 0 | 0 | 0 |
Add (-5 * row3) to row1
1 | -3 | 4 | -2 | 0 | -21 |
0 | 0 | 1 | 3 | 0 | 4 |
0 | 0 | 0 | 0 | 1 | 5 |
0 | 0 | 0 | 0 | 0 | 0 |
Add (-4 * row2) to row1
1 | -3 | 0 | -14 | 0 | -37 |
0 | 0 | 1 | 3 | 0 | 4 |
0 | 0 | 0 | 0 | 1 | 5 |
0 | 0 | 0 | 0 | 0 | 0 |
[ 2 4 -2 11 4. (20pts) Consider a matrix A = 3 7 -8 6 and corresponding Col A & Nul A. -2 -5 7 3 Col A is a subspace of Rk and Nul A is a subspace of R'. |(1) Find k and one nonzero-vector in Col A. | (2) Find 1 and one nonzero-vector in Nul A.
if whoever answers this could be detailed with explanations please! 1 -3 -2 -5 -14 -6-3-8 -21 2 8.(15 pts. total) M= is row equivalent to -2 6 1 4 5 -9 -2-7 -14 + (1-3 0-1 0 0 0 2 7 2 Pivels L 0 0 0 0 0 0 0 0 0 0 (a) Find k and/ so that Nul Mc R and Col Mc R (b) Without calculations, list rank M and dim Nul M. (c) Find...
Problem 1 Let A= 3 2 13 1 5 7 11 8 -3 9 10 -6 -4 12 8 a) [4 pts) Find a basis for N(A) in rational format. b) (3 pts) Find a particular solution to the matrix equation A*x= 5 -2 14 c) [3 pts] Use your answers in a), b) and the Superposition Principle to express the general solution in vector form to the matrix equation in b).
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A). Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
12. Find bases for Nul A and Col A. (8pts) WA 5 -3 1 1 1 - 1 2 22 5 0 - 8 - 2 4 -4 8 3 - 2
1 2 0 42 3 40 -80 64 48 -288 40 13 26 21-15 94-13) and 5 10 8-6 365 2 4 0 8 -6 -10 0 13 2-1 3·Let A = C 4 8 3 25 -2 9 5 1 42 3-1 9 10 22846-2 18 4 -4 3 21 3 2 334 15 26-2 14 5 48 -2 -10 -2 8 -8 814 16 28-23 148 36-6 56 (a) Find a basis for Nul (A)nNul (C) (b) Find...
Find the bases for Col A and Nul A. and then state the dimension of these subspaces for the matrix A and an echelon form of A below. 1 3 8 -1 -3 1 3 8 -1 -3 2 7 200 -4 0 1 4 2 -3 - 12 - 36 2 13000 3 13 40 0 -11 000 Abasis for Col A is given by (Use a comma to separate vectors as needed.)
4 ? 31 NW Let A= 3 7 -8 6 a) Find a spanning set of Nul A. How about Col A? b) is ū in Nul A? Is u in Col A? c) is ù in Nul A? Is ū in Col A? d) Is Col A =İR ?
Given the following sets: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, Even numbers A = {2, 4, 6, 8, 10}; Odd number B = {3, 5, 7, 9}; Natural numbers N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and Prime numbers C = {2, 3, 5, 7} Find the following: a) A ∪ C b) A ∩ N c) A ’ d) B ∩ N e) B ∪ N f) C...
Question 3. (20 pts) Let A 3 2 3 9 -2 -6 4 8 -9 2 2 Find a basis for Col(A) and a basis for Nul(A).