GOAL Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace. Which of the subsets of P 2 given in Exercises 1 through 5 are subspaces of P 2 (see Example 16)? Find a basis for those that are subspaces. 5. { p ( t ) : p ( − t ) = − p ( t ) , for all t } .
GOAL Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace. Which of the subsets of P 2 given in Exercises 1 through 5 are subspaces of P 2 (see Example 16)? Find a basis for those that are subspaces. 5. { p ( t ) : p ( − t ) = − p ( t ) , for all t } .
Solution Summary: The author analyzes whether a subset of the P_2 is linearly independent.
Determine whether the statement below is true or false. Justify the answer. Given vectors v1, ..., vp in ℝn, the set of all linear combinations of these vectors is a subspace of ℝn.
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(1 point) Consider the vector space P2 of polynomials of degree at most 2. Let H be the subspace spanned by
2x² + x + 2, −2x² + x +5, and x².
a. The dimension of the subspace H is
b. Is {2x² + x + 2, −2x² + x + 5, x²} a basis for P₂?
choose
c. A basis for the subspace H is {
Enter a polynomial or a comma separated list of polynomials.
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