Question

Linear transformation L(x)=Dx that transforms the vector x=Linear transformation L(x)=Dx that transforms the(1,4) to the vector L(x)= (3,6) and x=(2,5) to vector L(x)= (0,9)

describe, referencing the linear transformation, how the entries of matrix D were determined.

Answer 1

-2 1

1 1

is matrix D

Explanation:

Given that linear transformation L(x)=Dx that transforms the vector x=Linear transformation L(x)=Dx that transforms the(1,4) to the vector L(x)= (3,6) and x=(2,5) to vector L(x)= (0,9)

Since two dimensional vectors are used D is a 2x2 matrix

Let D =
`\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]`

D*(1,4) = (a+4c, b+4d) = (2,5)

and D*(3,6) = (3a+6c, 3b+6d) = (0,9)

a+4c =2 and 3a+6c =0

Solving c =1 and a = -2

Similarly b+4d =5 and 3b+6d =9

Solving d=1 and b =1

Hence matrix D would be

-2 1

1 1