Answer to Question #91407 in Linear Algebra for Sajid

Question

Choose the correct answer.
Q. If F is a linear transformation from R2 to R and F(1,1)=2, F(1,0)=3, then F(2,3)=?
a. 3
b. 2
c. 1
d. -4

Answer 1

Solution

Since F is a linear transformation, then F(x,y)=αx+βy. Substitute F(1,1)=2, F(1,0)=3 into the equation:

α*1+β*1=2

α*1+β*0=3

We have

α+β=2

α=3.

Hence, β=-1.

Let us find F(2,3)=3*2+(-1)*3=6-3=3.

Answer: a. 3.