Explore BrainMass
Share

Explore BrainMass

    Vectors and Linear Algebra : Basis, Column Space and Rank

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

    2 1 -1 3 4
    1 0 -1 2 0
    A= 1 1 0 1 4
    4 2 -2 6 8

    Find the basis for the row space, column space of A; What is the rank of A?

    © BrainMass Inc. brainmass.com October 9, 2019, 3:44 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/vectors-linear-algebra-basis-column-space-rank-11557

    Solution Preview

    Well, the matrix is:

    The number of pivot columns in the rref(A) shows the number of linearly independent columns and if we pick the corresponding columns, they will form a basis for the column space of the given matrix. Therefore, we must find rref(A) using elementary row/column operations and we get:

    Well, only the first and second columns are the ...

    Solution Summary

    Basis, column space and rank are found for a matrix.

    $2.19