Consider the matrix Find the nullspace of A. Now finding a spanning set for the
ID: 3076786 • Letter: C
Question
Consider the matrix Find the nullspace of A. Now finding a spanning set for the nullspace of A.Explanation / Answer
a) for nullspace of A we need to solve AX = 0 where X = [x,y,z,t] we get -2x + 3y + z = 0 --->(1) x - y + z + t = 0 ----->(2) -x + 2y + 2z + t = 0------>(3) we get z = 2x - 3y from (1) t = 4y - 3x from (2) - (1) putting this in the last equation -x + 2y + 4x - 6y + 4y - 3x = 0 this is an identity which always holds.... therefore take x = arbitrary and y = arbitrary and put in the equation of z and t and get the respective values..... (b) X = [ x , y , 2x - 3y , 4y - 3x] = x[1,0,2,-3] + y[0,1,-3,4] therefore spanning set is { [1,0,2,-3] , [0,1,-3,4] }