A matrix N\displaystyle {N} was used to transform two vectors: P⃗=[10]\displaystyle \vec{{P}}={\left[\begin{array}{c} {1}\\{0}\end{array}\right]} and Q⃗=[1−1]\displaystyle \vec{{Q}}={\left[\begin{array}{c} {1}\\-{1}\end{array}\right]}, which are shown as open dots on the plane.

10-1010-10PP'QQ'

The results of transforming these points are shown as solid dots, P′=[3−3]\displaystyle {P}'={\left[\begin{array}{c} {3}\\-{3}\end{array}\right]} and Q′=[5−7]\displaystyle {Q}'={\left[\begin{array}{c} {5}\\-{7}\end{array}\right]}.

So, we have N[10]=[3−3]\displaystyle {N}{\left[\begin{array}{c} {1}\\{0}\end{array}\right]}={\left[\begin{array}{c} {3}\\-{3}\end{array}\right]} and N[1−1]=[5−7]\displaystyle {N}{\left[\begin{array}{c} {1}\\-{1}\end{array}\right]}={\left[\begin{array}{c} {5}\\-{7}\end{array}\right]}.

Find the matrix N\displaystyle {N}.

Answer: N=\displaystyle {N}=
 
 
 

What would be the result of N[01]\displaystyle {N}{\left[\begin{array}{c} {0}\\{1}\end{array}\right]}?

Answer: N[01]=\displaystyle {N}{\left[\begin{array}{c} {0}\\{1}\end{array}\right]}=
 
 
 

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