Explore BrainMass
Share

Explore BrainMass

    vector spaces and linear spans

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Find all real numbers k such that the vector v=(1,-2,k) in R^3 (with the usual operations) is
    in the linear span of the vectors x=(3,0,-2) and y=(2,-1,-5).
    Prove your answer. Be sure to address both necessity and sufficiency. Show all work.

    © BrainMass Inc. brainmass.com October 10, 2019, 3:57 am ad1c9bdddf
    https://brainmass.com/math/vector-calculus/vector-spaces-linear-spans-443497

    Attachments

    Solution Preview

    Find all real numbers k such that the vector v=(1,-2,k) in R^3 (with the usual operations) is
    in the linear span of the vectors x=(3,0,-2) and y=(2,-1,-5).
    Prove your answer. Be sure to address both necessity and sufficiency. Show all work.

    If the given vector v to be in the linear span of the vectors x and y, we should have some scalars a and b such that v=ax+by
    This gives the relation ...

    Solution Summary

    This solution carefully addresses vector spaces and linear spans.

    $2.19