Homework SourseGiven the vectors v 1 1 1 w 1 0 1 F 1 2 3 G 0 1 0 0 0 0
Given the vectors v = [1 1 1], w = [1 0 1], F = [1 2 3], G = [0 1 0], 0 = [0 0 0] and the sets A = {v, w} B = {v, w, F} C = {v, w, G} D = {v, w, F, G}, Z = {0} name all the linearly independent sets name the sets which span R^3 name any sets which form a basis for R^3
![Given the vectors v = [1 1 1], w = [1 0 1], F = [1 2 3], G = [0 1 0], 0 = [0 0 0] and the sets A = {v, w} B = {v, w, F} C = {v, w, G} D = {v, w, F, G}, Z = {0}](/WebImages/46/given-the-vectors-v-1-1-1-w-1-0-1-f-1-2-3-g-0-1-0-0-0-0-1146599-1761616398-0.webp "Given the vectors v = [1 1 1], w = [1 0 1], F = [1 2 3], G = [0 1 0], 0 = [0 0 0] and the sets A = {v, w} B = {v, w, F} C = {v, w, G} D = {v, w, F, G}, Z = {0}")
![Given the vectors v = [1 1 1], w = [1 0 1], F = [1 2 3], G = [0 1 0], 0 = [0 0 0] and the sets A = {v, w} B = {v, w, F} C = {v, w, G} D = {v, w, F, G}, Z = {0}](/WebImages/46/given-the-vectors-v-1-1-1-w-1-0-1-f-1-2-3-g-0-1-0-0-0-0-1146599-1761616398-1.webp "Given the vectors v = [1 1 1], w = [1 0 1], F = [1 2 3], G = [0 1 0], 0 = [0 0 0] and the sets A = {v, w} B = {v, w, F} C = {v, w, G} D = {v, w, F, G}, Z = {0}")
Solution
Let A =
1
1
1
0
1
0
2
1
1
1
3
0
We will reduce A to its RREF as under:
Add -1 times the 1st row to the 2nd row
Add -1 times the 1st row to the 3rd row
Multiply the 2nd row by -1
Multiply the 3rd row by ½
Add 1 times the 3rd row to the 2nd row
Add -1 times the 3rd row to the 1st row
Add -1 times the 2nd row to the 1st row
Then the RREF of A is:
1
0
0
1
0
1
0
-1
0
0
1
0
Thus:
| 1 | 1 | 1 | 0 |
| 1 | 0 | 2 | 1 |
| 1 | 1 | 3 | 0 |
