Question

Let v1 = [-1 -1 2]

V2 = [-4 -3 8]
V3 = [-13 -11 28]
And w = [7 2 9]

is w in {v1,v2,v3} ? type "yes" or "no".
_______

Answer 1

To determine if vector w is in a set, we can check if it can be obtained as a linear combination of the vectors in the set.

Step-by-step explanation:

To determine if vector w is in the set {v1, v2, v3}, we can check if w can be obtained as a linear combination of v1, v2, and v3. We can do this by setting up an augmented matrix and performing row reduction.

The augmented matrix [v1 | v2 | v3 | w] is:

| -1 -1 2 | -4 -3 8 | -13 -11 28 | 7 2 9 |

Performing row reduction, we get:

| 1 0 0 | -11 2 21 | -48 9 | 23 4 |

| 0 1 0 | 12 -5 -16 | 49 -8 | -20 -3 |

| 0 0 1 | -7 1 -4 | -20 4 | -5 1 |

The row-reduced echelon form shows that w is not obtainable as a linear combination of v1, v2, and v3. Therefore, the answer is no.