Question

Determine if ~w = (−4, 6, 1) is a linear combination of ~u = (1, 0, −1) and
~v = (1, −11, 3) . If so, then express ~w as a linear combination of ~u and ~v .

Let ~u = (1, 1, −1) and ~v = (2, 1, 3). Determine if ~w = (7, 6, 3) is a linear
combination of ~u and ~v. If so, express ~w as a linear combination of ~u and ~v.

Let
~x1 = (2, −1, 3, 1), ~x2 = (1, 0, −1, 1), ~x3 = (0, 1, 4, 2).
(i) Determine if ~x1, ~x2, and ~x3 are linearly independent. Justify your answer.
(ii) Determine if ~v = (2, −1, 3, 1) is a linear combination of ~x1, ~x2, and ~x3.
If so, express ~v as a linear combination of ~x1, ~x2, and ~x3. If not, justify
your answer.
(iii) Determine if ~u = (1, 0, 0, 1) is a linear combination of ~x1, ~x2, and ~x3. If
so, express ~u as a linear combination of ~x1, ~x2, and ~x3. If not, justify
your answer.

Answer 1