Please Complete Number 32 Only. Thank You In Exercises 23-34, determine whether
ID: 2942933 • Letter: P
Question
Please Complete Number 32 Only. Thank You
In Exercises 23-34, determine whether the set S is linear, independent or linearly dependent. S = {(-2, 2), (3, 5)} S = {(-2, 4), (1, -2)} S = {(O, 0), (1, -1)} S = {(1, 0), (1, 1), (2, -0)} S = {(1, -4, 1), (6, 3, 2)} S = {(6, 2, 1), (-1, 3, 2)} S = {(1, 1, 1), (2, 2, 2), (3, 3, 3)} S = {(3/4, 5/2, 3/2), (3, 4, 7/2), (-3/2, 6, 2)} S = {(-4, -3, 4), (1, -2, 3), (6, 0, 0)} S = {(1, 0, 0), (0, 4, 0), (0, 0, -6), (1, 5, -3)} S = {(4, -3, 6, 2), (1, 8, 3, 1), (3, -2, - 1, 0)}Explanation / Answer
32)
Place vectors in a 4x3 matrix
1 0 0
0 4 0
0 0 -6
1 5 -3
Perform row reduction
Add (-1 * row1) to row4
1 0 0
0 4 0
0 0 -6
0 5 -3
Divide row2 by 4
1 0 0
0 1 0
0 0 -6
0 5 -3
Add (-5 * row2) to row4
1 0 0
0 1 0
0 0 -6
0 0 -3
Divide row3 by -6
1 0 0
0 1 0
0 0 1
0 0 -3
Add (3 * row3) to row4
1 0 0
0 1 0
0 0 1
0 0 0
Clearly all 4 vectors are not linearly independent because the last row are all zeroes