Question

describe explicitly the linear transformation T:R2-R2 such that T (2,3)=(4,5)and T(1,0)=(0,0).​

Answer 1

describe explicitly the linear transformation T:R2-R2 such that T (2,3)=(4,5)and T(1,0)=(0,0).

T(x1 , x2) = (y1 , y2)

y1 = ax1 + b

4 = 2a + b eq1

0 = a + b eq2

eq1 - eq2

a= 4

b = -4

y1 = 4x1 - 4

y2 = cx2 + d

5 = 3c + d

0 = 0 + d

d = 0

c = 5/3

y2 = 5x2/3

T(x1,x2) = (4x1 -4 , 5x2/3)