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Flashcards in a4,,5 Deck (14):
1

Hx = c is inconsistent

H|c has a row of all zeros to a partition of non zero

2

if Hx=c is consistent and has a pivot in every column

the solution is unique

3

Hx=c is consistent and H has columns without pivots

the solution set is infinite with many free variables as there are pivot free columns in H

4

A is invertible if

AC = CA = I

5

if something is not invertible it is

singular

6

conditions for A-1 to exist

A is invertible
A is row equivelent to nxn identity matrix I
Ax = b has a solution for each column vector b in Rn
A can be expressed as a product of elementary matrices
Span of row and column vecotrs in Rn

7

nullspace of a m x n matrix

nullspace of A is the set of all solutions to Ax = 0
N = { x in Rn | Ax = 0}

8

row space

span of rowvectors of A

9

column space

span of column vectors

10

if rv1 rvk = 0 has 1 solution

lineraly independant

11

if rv1 rvk = 0 has more than 1

linerarly dependent

12

definition of subspace

W is non empty, if u and v are in W u+v are in W
and ru in W

13

principal

size

14

argument

angle