Due Thurs (1119)
- Orientation assignment
- HW 1.1
(X, X,...a) Linear Equation: one that can be
written in the form:
Citi & Ce Ket... + Can = b
↑
coefficients (real#s)
Ex: 2x, + 3×2 = 7
- ✗it ½xz-✗ 3 = 11
System of Equations: Multiple linear
equations in same variables
Ex: Six,-✗2=5
3×1 + X2 = I
2x.-✗ 2=5
+
3x, + ✗ 2 = / 3(5) txz=l
1 8 ×2=1151
5-1
Sx, = 6
5 S -¥ -⅓
I 1=65
✗ 2 =-Bg
,Consistent: System w/@least I solution
- I solution, many solutions, etc. Q: Is EF
inconsistent: system w/no solution [2416
- 2 30
Q: Does a solution exist?
② Is that solution unique? (is it the only one?) NOTE: Any
Matrix is now
MX h equivalent t
row column input many E
matrices.
Echelon Form A rectangular matrix is in
echelon form if:
Reduct
① All non-Zero rows are above. any Zero rows.
How to
② Each leading non-Zero entry of a row is in
, Vector: ordered list of #s Linear Combination
(5,0) (3,211) (¾ Have vectors ,Ja,-
Then:
Two Vectors not equal: C.lit Cziet..-tepi
(Scalars (weights) C
(8) + (s)
Vectors in 15h"
R"-1:?)/ aier to all isia.nl Ex.
(all poss. Vectors w/n entries) l Choose any sca
Adding vectors: Scale Vectors:
linear comb. of
* Must be same size* ☒¾ Julti. each entry by scalar
Z 13
-
7
-
:)
( ☐ f) + ☐ E.
Scalar
(must be
add component by component a real #)
- Orientation assignment
- HW 1.1
(X, X,...a) Linear Equation: one that can be
written in the form:
Citi & Ce Ket... + Can = b
↑
coefficients (real#s)
Ex: 2x, + 3×2 = 7
- ✗it ½xz-✗ 3 = 11
System of Equations: Multiple linear
equations in same variables
Ex: Six,-✗2=5
3×1 + X2 = I
2x.-✗ 2=5
+
3x, + ✗ 2 = / 3(5) txz=l
1 8 ×2=1151
5-1
Sx, = 6
5 S -¥ -⅓
I 1=65
✗ 2 =-Bg
,Consistent: System w/@least I solution
- I solution, many solutions, etc. Q: Is EF
inconsistent: system w/no solution [2416
- 2 30
Q: Does a solution exist?
② Is that solution unique? (is it the only one?) NOTE: Any
Matrix is now
MX h equivalent t
row column input many E
matrices.
Echelon Form A rectangular matrix is in
echelon form if:
Reduct
① All non-Zero rows are above. any Zero rows.
How to
② Each leading non-Zero entry of a row is in
, Vector: ordered list of #s Linear Combination
(5,0) (3,211) (¾ Have vectors ,Ja,-
Then:
Two Vectors not equal: C.lit Cziet..-tepi
(Scalars (weights) C
(8) + (s)
Vectors in 15h"
R"-1:?)/ aier to all isia.nl Ex.
(all poss. Vectors w/n entries) l Choose any sca
Adding vectors: Scale Vectors:
linear comb. of
* Must be same size* ☒¾ Julti. each entry by scalar
Z 13
-
7
-
:)
( ☐ f) + ☐ E.
Scalar
(must be
add component by component a real #)
