Find a basis for the column space of the matrix Find a basis

Find a basis for the column space of the matrix. Find a basis for Col B = [1 1 0 -2 0 0 0 0 1 4 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0] [1 0 0 0], [0 1 0 0], [0 0 1 0], [0 0 0 1] [1 0 0 0 0 0], [1 0 0 0 0 0], [0 1 0 0 0], [-2 4 0 0 0], [0 0 1 0 0], [0 0 0 1 0] [1 0 0 0 0], [0 1 0 0 0], [0 0 1 0 0], [0 0 0 1 0] [1 0 0 0 0], [0 0 1 0 0], [0 0 0 1 0] Determine whether the set of vectors is a basis for R^3.

Solution

B matrix is in row echelon form . Column space is set of all columns in B which contains leading pivot elements in echelon form . So answer is C