Practice Midterm #7
How do we show that the function is linear? Do we just need to show that we can get each part of the vector independently of each other (get a by itself, b by itself, and c by itself)? Or do we need to show that the function holds under addition and multiplication ((T(a+b) = T(a) + T(b), kT(a,b) = T(k(a,b))?
carlintou: May 3, 2015, 7:38 p.m.
Oops, I meant that to be Practice Midterm #4
richardsun: May 3, 2015, 10:51 p.m.
We just need to prove the addition and multiplication properties. A function can be linear even if the result doesn't span the whole vector space.
dyana: May 4, 2015, 3:25 p.m.
I got that a) is linear, b) is not, and c) is linear. How do you set up the matrix for d) so we can row reduce to check for linear dependence?
valerie: May 4, 2015, 9:18 p.m.
I got that c) is not linear because it is not closed under scalar multiplication.
dyana: May 5, 2015, 4:14 p.m.
yeah, my bad. It was not linear