Thread: Linear algebra find the basis

I've been stuck on the following two problems for a while, so any help would be appreciated!

For each of the two cases below, find the dimension of V by using an appropriate method to create a basis. (Note that the E stands for epsilon)

a) V = span({x^4 - x^3 + 2x^2, 2x^4 + x - 5, 2x^3 - 4x^2 + x - 4, 6, x^2 - 1})

b) V = {p E P_6 | p = ax^6 - bx^5 + ax^4 - cx^3 + (a+b+c)x^2 - (a - c)x + (3a - 2b - 16c), for real numbers a, b, and c

Originally Posted by buckaroobill

I've been stuck on the following two problems for a while, so any help would be appreciated!

For each of the two cases below, find the dimension of V by using an appropriate method to create a basis. (Note that the E stands for epsilon)

a) V = span({x^4 - x^3 + 2x^2, 2x^4 + x - 5, 2x^3 - 4x^2 + x - 4, 6, x^2 - 1})

Since adding polynomial can be thought of adding Euclidean vectors we can find row space of:
[1 -1 2 0 0]
[2 0 0 1 -5]
[0 2 -4 1 -4]
[0 0 1 0 -1]
By Gaussian Elimination.

In the second problem write it as a matrix.