A First Course in Linear Algebra · Problem SS.C50

Vectors — Robert Beezer

Mathematics — Linear Algebra · spanning-sets-null-spaces

Problem

Let

A

be the matrix below. 1. Find a set

S

so that

\mathcal{N}(A) = \langle S \rangle

. 2. If

\mathbf{z} = \begin{bmatrix} 3 \\ -5 \\ 1 \\ 2 \end{bmatrix}

, then show directly that

\mathbf{z} \in \mathcal{N}(A)

. 3. Write

\mathbf{z}

as a linear combination of the vectors in

S

A = \begin{bmatrix} 2 & 3 & 1 & 4 \\ 1 & 2 & 1 & 3 \\ -1 & 0 & 1 & 1 \end{bmatrix}