Question

1 - 2 Sketch the span of the columns of A= to Až = 7 and its span. ). On the same grid sketch a non-zero solution -8) 12 11

Answer 1

Clearly, the columns of $\mathbf{A}$ are

$\begin{bmatrix} 1\\ 4 \end{bmatrix}$ and

CON

which are linearly dependent as

$\begin{bmatrix} -2\\ -8 \end{bmatrix} = -2\begin{bmatrix} 1\\ 4 \end{bmatrix}$

Thus, the span of the columns of can be plotted as

s + - | 10 x1 心-6

Now, consider a vector $\vec{x} = \begin{bmatrix} x \\ y \end{bmatrix}$ that satisfies then,

AT = 0

I – 2y = 0 4.1 – 8y = 0

Clearly, the solutions of the equations correspond to all such that

O, Y ER

I = 2y

This corresponds to the vectors of the form

=1

Thus we can plot the span of the solutions as

必6 -10 10