MTH1004 Linear Algebra Practical Class 1

Question 1

Question

Determine whether the following vectors are linearly independent: (i) $u=\left(\begin{array}{c}3\\ 1\end{array}\right)$, $v=\left(\begin{array}{c}0\\ -1\end{array}\right)$, (ii) $u=\left(\begin{array}{c}2\\ -1\end{array}\right)$, $v=\left(\begin{array}{c}-1\\ -1\end{array}\right)$

Solution

…

Question 2

Question

Find a value for x so that the following vectors: $u=\left(\begin{array}{c}1\\ 1\end{array}\right)$, $v=\left(\begin{array}{c}1\\ x\end{array}\right)$ are: (i) linearly dependent. (ii) linearly independent.

Solution

…

Question 3

Question

Find two nontrivial vectors (other than ${\mathbf{e}}_1,{\mathbf{e}}_2$) that span the plane.

Solution

…

Question 4

Question

Show that the vectors: $u=\left(\begin{array}{c}-1\\ 1\end{array}\right)$, $v=\left(\begin{array}{c}1/3\\ -1/3\end{array}\right)$ are linearly dependent.

Solution

…

Question 5

Question

Determine whether the vector $u=\left(\begin{array}{c}1\\ 2\end{array}\right)$ is a linear combination of: $v=\left(\begin{array}{c}0\\ 2\end{array}\right)$, $w=\left(\begin{array}{c}1\\ 4\end{array}\right)$ If yes, find the scalars.

Solution

…