SOLUTION: A. Write down the matrix M of the linear transformation M: (x,y)---->(kx+y, 3x+ky) B. If the image of (-1, 2) under M is (a. -7), find the value of a THANK YOU

Algebra ->  Matrices-and-determiminant -> SOLUTION: A. Write down the matrix M of the linear transformation M: (x,y)---->(kx+y, 3x+ky) B. If the image of (-1, 2) under M is (a. -7), find the value of a THANK YOU      Log On


   

Question 1017823: A. Write down the matrix M of the linear transformation
M: (x,y)---->(kx+y, 3x+ky)
B. If the image of (-1, 2) under M is (a. -7), find the value of a
THANK YOU
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%22M%3A%22%28matrix%281%2C3%2Cx%2C%22%2C%22%2Cy%29%29%22----%3E%22%28matrix%281%2C3%2Ckx%2By%2C%22%2C%22%2C3x%2Bky%29%29

%22M%3A%22%28matrix%281%2C3%2C-1%2C%22%2C%22%2C2%29%29%22----%3E%22%28matrix%281%2C3%2Ck%28-1%29%2B2%2C%22%2C%22%2C3%28-1%29%2Bk%282%29%29%29%22%22=%22%22%28matrix%281%2C3%2C-k%2B2%2C%22%2C%22%2C-3%2B2k%29%29

Given:

%22M%3A%22%28matrix%281%2C3%2C-1%2C%22%2C%22%2C2%29%29%22----%3E%22%28matrix%281%2C3%2Ca%2C%22%2C%22%2C-7%29%29

Therefore:


%28matrix%281%2C3%2C-k%2B2%2C%22%2C%22%2C-3%2B2k%29%29%22%22=%22%22%28matrix%281%2C3%2Ca%2C%22%2C%22%2C-7%29%29

   -k+2 = a, -3+2k = -7
                2k = -4
                 k = -2

-(-2)+2 = a  
    2+2 = a
      4 = a

Edwin