Summary Ma100 LT exam notes

,
, Chapter 17

Vector space

non-empty
·


8
(f g((): f(x) g(x)
+ =
+




·
(2f)(x) x f(x) =
=




Subspaces
·
non-empty
under f(k 1) f(x) f() +
1,Iew, 16
=


close
+



·
+




close under 0
·
xf() f(x) =
NEW, CEN


Chapter 18

(inX)=(in E1,
-Linear Span= 3 G2, 4 22V2+...+ 2143, Vi GV E,.
= +



, . .

.,



-
X spans V if (in(X) =
v



4.4 +22k x, b
=


+ ...+


A (4x..)=
(i)
= =




A
= b

(A1b) solution then spans IR-
↳ A full row rank

-
Linear independence iff

2,V1 xzV ...+2x4 0
+ =
+




has unique solution x, x2=...=c1 0
= =




dependent if all
not 0
=




A full column rank