Consider the following vectors {1 + x + x^2, 1 - x^2, x + 2, 1...

Consider the following vectors {1 + x + x^2, 1 - x^2, x + 2, 1 - x}.
a) Test or refute if the vector set is linearly independent?
b) Construct a linearly independent set of dimension 2, describe the
shape of the generated space.
c) Construct a linearly independent set of dimension 3, describe the
shape of the generated space.
d) For the base you chose in part c), find a linear combination for
p (x) = 3 + 11x + 8x^3

Expert Solution

Colby Messinger answered 2 years ago

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