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Math Help - Linear algebra find the basis

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by buckaroobill View Post
    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.
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  3. #3
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    In the second problem write it as a matrix.
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