Shared Flashcard Set

Details

math415 UIUC
math415 sp19
18
Mathematics
Undergraduate 1
02/06/2019

Additional Mathematics Flashcards

 


 

Cards

Term
Echelon Form - Requirements
Definition
All 0 rows are at the bottom.
Leading entry is to right of leading coeff in row above
All entries below a "pivot" are 0
Term
Reduced Row Echelon Form
Definition
REF + #'s above are nonzero + pivots are 1
Term
Locate pivot columns
Definition
Do row ops until in REF
Term
Pivot variables and free variables
Definition
Pivots - variables that are pivots (x1,x2,etc) in the RREF matrix. Free variables - every other variable
Term
A linear system is consistent if ___
Definition
Does not have a row like [0,0,0 | b] (b is a non zero number).

0x+0y+0z≠b
Term
Linear combination
Definition
Can combine scalars with vectors.

c1A+c2B+c3C = D

to get another vector
Term
Span(v) geometrically
Definition
Span(v) is the set of all vectors of the form c*v
Term
Span(v1,v2)
Definition
Span(v1,v2) is the collection of all vectors in the direction of v1 or v2
Term
Span(u,v) for plane vs line situation
Definition
Is v a multiple of u? Yes - span line. No? Span plane.
Term
Determine if w is in Span(u,v) (u,v,w are vectors)?
Definition
Check if linear system corresponding to u,v|w is consistent (write as augmented form with vectors as columns)
Term
a_ij is the__
Definition
ith row, jth column
Term
m x n matrix (columns, rows)
Definition
n columns, m rows
Term
Matrix Transpose
Definition
Swap rows and columns
Term
Symmetric Matrix
Definition
The matrix is equal to it's transpose
Term
Solve system with LU decomp
Definition
If Ax=b, then

Lc=b -> Ux=c
Term
Vector Space
Definition
set of objects I can linear combine

(ex: matricies, polynomials)
Term
Subspace H of V
Definition
It's a subspace of V if:
H is a subset of V if:

It shares a 0 vector with V
Sums of things in H are in H
cU is in H if U is in H
Term
LU decomp
Definition
1) Find U using rowops

2) Take the opposite sign of row ops and insert correctly.
Supporting users have an ad free experience!