Q:

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.

Accepted Solution

A:
Answer:-2   11   1is matrix DStep-by-step 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 matrixLet D = [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]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 =0Solving c =1 and a = -2Similarly b+4d =5 and 3b+6d =9Solving d=1 and b =1Hence matrix D would be-2   11   1