Systems of linear eq Flashcards
(13 cards)
1
Q
If constants r not = to 0
A
System is non homogenous
2
Q
All constants r = to 0
A
System is homogenous
3
Q
Are homogeneous system consistent?
A
Yes, always
4
Q
Rank of A?
A
of non0 rows in the REF of A
5
Q
If rank(A) = rank([A|B])
A
System is consistent: has a solution
Otherwise, inconsistent: no solution
6
Q
r = n
A
System has a unique sol
7
Q
r < n
A
Infinitely many sol
8
Q
r > n
A
No sol
9
Q
If AX=B is homogenous, the sol X = (0,0,..0) is called the ____ sol of AX=B
A
Trivial, other sol r called nontrivial
10
Q
If r = n (1 unique sol) & homogeneous then what is its sol?
A
Trivial
11
Q
If A has an inverse, then the sol of system is?
A
Unique
12
Q
Methods for solving systems
A
Matrix inversion
Gauss Jordan reduction
13
Q
Requirements for matrix inversion?
A
Matrix must have an inverse
