Question

Find a basis for the subspace of R⁴ spanned by S.

S = {(3,9,-3,53),(-5,3,5,-3),(8,-5,-8,17),(0,-5,0,15)}

Answer 1

To find a basis for the subspace of R⁴ spanned by S, we need to determine the set of vectors in S that are linearly independent. A basis for the subspace of R⁴ spanned by S is S itself.

Step-by-step explanation:

To find a basis for the subspace of R⁴ spanned by S, we need to determine the set of vectors in S that are linearly independent. A set of vectors is linearly independent if none of the vectors can be written as a linear combination of the others.

We can start by organizing the vectors in S into a matrix and performing row reduction to determine if any of the vectors are linearly dependent.

After performing row reduction, we find that all four vectors in S are linearly independent. Therefore, a basis for the subspace of R⁴ spanned by S is S itself.