Linear Algebra Fundamentals

Question 1

A $2	imes2$ matrix has determinant $-2$. Geometrically, what does this tell you about the linear transformation?

Accepted Answer

c1

Answer

It reverses orientation and scales area by $2$

Answer

It preserves orientation and scales area by $-2$

Answer

It reverses orientation and scales area by $-2$

Answer

It preserves orientation and scales area by $2$

Question 2

If $\mathbf{u}=(1,2)$ and $\mathbf{v}=(3,-1)$, what is $\mathbf{u}+\mathbf{v}$?

Accepted Answer

c1

Answer

$(4,1)$

Answer

$(3,1)$

Answer

$(-2,3)$

Answer

$(2,1)$

Question 3

Which matrix represents a $90^\circ$ counterclockwise rotation in $\mathbb{R}^2$?

Accepted Answer

c3

Answer

$\begin{pmatrix}-1 & 0\0 & -1\end{pmatrix}$

Answer

$\begin{pmatrix}0 & 1\-1 & 0\end{pmatrix}$

Answer

$\begin{pmatrix}0 & -1\1 & 0\end{pmatrix}$

Answer

$\begin{pmatrix}1 & 0\0 & -1\end{pmatrix}$