A First Course in Linear Algebra · Problem C60

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · column-space-descriptions

Problem

For the matrix BB below, find sets of vectors whose span equals the column space of BB (C(B)\mathcal{C}(B)) and which individually meet the following extra requirements. 1. The set illustrates the definition of the column space. 2. The set is linearly independent and the members of the set are columns of BB. 3. The set is linearly independent with a ``nice pattern of zeros and ones'' at the top of each vector. 4. The set is linearly independent with a ``nice pattern of zeros and ones'' at the bottom of each vector. B=[23111101−123−4]B = \begin{bmatrix} 2 & 3 & 1 & 1 \\ 1 & 1 & 0 & 1 \\ -1 & 2 & 3 & -4 \end{bmatrix}

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