Math 220 Assignment

September 21, 2001

Assignment for Monday, September 24

1. Prepare for the short quiz, which has been deferred.

2. Let C be the 4 \times 4 matrix

   ( 1  2 0 2 -2 -1 3 2 -2 2 6 -1 1 0 -2 0 )

   ,

   and let f be the linear map (or function) from R^{4} to R^{4} defined by the formula

   y  =  f(x)  =  C x  .

   1. Find all solutions of f(x) = (0, 0, 0, 0).

   2. Find all solutions of f(x) = (1, -2, -2, 1) with x_{3} = 0.

   3. Find all solutions of f(x) = (1, -2, -2, 1).

   4. Find all solutions of f(x) = (-1, -7, 2, 1) with x_{3} = 0.

   5. Find all solutions of f(x) = (-1, -7, 2, 1).

   6. What is the kernel of f ?

   7. Find equations that characterize the image of f.

3. Let M be an m \times n matrix, and let phi(x) = M x. Let a and b be any two points of R^{n}. Show that phi(a) = phi(b) if and only if a - b lies in the kernel of phi.

AUTHOR  |  COMMENT