Practice Midterm #2
ruiqihuang
Find a set of vectors that span the image of the linear transformation. Find a set of vectors that span the kernel of the linear transformation rref the following: [1 2 1 ] [3 -2 4 ] [1 -6 2 ] [1 2 1] [0 -8 1] [0 -8 1] [1 2 1] [0 -8 1] [0 0 0] [4 0 5] [0 -8 1] [0 0 0] [1 0 5/4] [0 1 -1/8] [0 0 0] Column 1 and Column 2 present leading one's, so they are considered as vectors that span the image of the linear transformation. [1] (correspond to) [0] vector{1,3,1} [0] [0] (correspond to) [1] vector{2,-2,-6} [0] Whereas, column 3 demonstrate a linear relation with both vector 1 and vector 2, meaning it span the kernel of linear transformation. [ 5/4 ] [-1/8 ] ----> $x_{3}$ = (5/4) $x_{1}$ + (-1/8) $x_{2}$ [ 0 ] 0 = (5/4) $x_{1}$ + (-1/8) $x_{2}$ - $x_{3}$ using the equation derived from linear relation, we can rewrite it as a vector that span the kernel vector( $/frac{5}/{4}$ , $/frac {-1}/{8}$ , 1} Ruiqi Huang Disc 3B
ruiqihuang: May 6, 2015, 11:01 a.m.
sorry this is solution to number 5