Garis y=2x-5 ditransformasikan oleh transformasi yang bersesuaian dengan matriks baris 1 (2 3) baris 2 (1 4). persamaan bayangan garis tersebut adalah ...

jawab

y = 2x - 5

[tex] \left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}2&3\\1&4\end{array}\right]\, \left[\begin{array}{ccc}x\\y\end{array}\right] [/tex]

[tex] \left[\begin{array}{ccc}x\\y\end{array}\right]\,=\, \frac{1}{2(4) -1(3)} \left[\begin{array}{ccc}4&-3\\-1&2\end{array}\right]\, \left[\begin{array}{ccc}x'\\y'\end{array}\right] [/tex]

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right]\,=\, \frac{1}{5} \left[\begin{array}{ccc}4&-3\\-1&2\end{array}\right]\, \left[\begin{array}{ccc}x'\\y'\end{array}\right][/tex]


x = 1/5 (4x' - 3y')
y = 1/5 (-x' + 2y')
subs ke  y = 2x - 5

1/5 ( - x' + 2y' ) = 2(1/5)(4x' - 3y')  - 5....kalikan 5
x - 2y = 2(4x - 3y) - 25
x - 2y = 8x - 6y - 25
x - 8x  - 2y + 6y = - 25
-7x     + 4y = - 25
4y = 7x - 25