Answer:
T(u1) = [tex]\left[\begin{array}{c}-22\\2\end{array}\right][/tex], T(u2) = [tex]\left[\begin{array}{ccc}-2\\-40\end{array}\right][/tex]
Step-by-step explanation: Matrix A = [tex]\left[\begin{array}{ccc}4&2\\-5&6\end{array}\right][/tex], u1 = [tex]\left[\begin{array}{ccc}-4\\-3\end{array}\right][/tex], u2 = [tex]\left[\begin{array}{ccc}2\\-5\end{array}\right][/tex]
If T(x) = Ax and it wants to find T(u1), it means
T(u1) = [tex]\left[\begin{array}{ccc}4&2\\-5&6\end{array}\right][/tex] · [tex]\left[\begin{array}{ccc}-4\\-3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}4.(-4)+2.(-3)\\(-5).(-4)+6.(-3)\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-22\\2\end{array}\right][/tex]
To find T(u2):
T(u2) = [tex]\left[\begin{array}{ccc}4&2\\-5&6\end{array}\right][/tex] · [tex]\left[\begin{array}{ccc}2\\-5\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}4.2+2.(-5)\\(-5).2+6(-5)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2\\-40\end{array}\right][/tex]
