,
, 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
, 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
