A First Course in Linear Algebra · Problem C26

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · extended-echelon-form-four-subsets

Problem

For the matrix

D

below use the extended echelon form to find: 1. A linearly independent set whose span is the column space of

D

. 2. A linearly independent set whose span is the left null space of

D

D = \begin{bmatrix} -7 & -11 & -19 & -15 \\ 6 & 10 & 18 & 14 \\ 3 & 5 & 9 & 7 \\ -1 & -2 & -4 & -3 \end{bmatrix}