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