Question

If C is an mxn matrix prove that:

Answer 1

\[dimRowA+\dim(NulA^t)=m\]

Answer 2

big danny boy. long time no speak

Answer 3

hey ya !

Answer 4

that should be A not C

Answer 5

i went on a hiatus during my classes

Answer 6

lol why?

Answer 7

it was super rush!!

Answer 8

whats that?

Answer 9

they really packed that course in

Answer 10

and u just let off at the lecturer?

Answer 11

what nonono

Answer 12

looool

Answer 13

i mean that why i havent been on here

Answer 14

ohhhhhh yea. same i got fair bit of stuff to do myself.

Answer 15

you had summer classes too?

Answer 16

or winter classes i guess in australia

Answer 17

what does dim mean?

Answer 18

need someone to answer this question and oldrinbataku is not online.

nah this is not winter nor summer. its just in the normal uni slot

Answer 19

we are in week 4

Answer 20

8 weeks and summer sets in

Answer 21

T_T

Answer 22

i got 15 days left till classes

Answer 23

what does dim mean there?

Answer 24

dimension

Answer 25

i was afraid of that

Answer 26

hahaha

Answer 27

lol

Answer 28

is that nul supposed to be short for nul space?

Answer 29

yup

Answer 30

ideas?

Answer 31

i dont get the question lol

Answer 32

dimension of null space of a transform?

Answer 33

what if your null space as rows and colums

Answer 34

has

Answer 35

its rows and columns no transform.

Answer 36

ok so is your question like this
dimension of the rows of A + the dimension of the null spaces' rows and columns = m

Answer 37

the dimnesion of the null space of columns and rows since its transopsed

Answer 38

okay umm soo wont your null space just be a long vector with 1 column = m rows

Answer 39

i think u gotta know the fact that \[rankA+dimNulA=n\]

Answer 40

thats the theorem

Answer 41

throwing random bits of linear algebra ive been learning lately so umm

Answer 42

then wouldnt the N = |-F |
| I |

Answer 43

the size of F depending on the columns - number of pivots or rank of A

Answer 44

nah i think i got it.
u are being too practical haha

Answer 45

lmao i like to think i helped

Answer 46

bro i dont know anything about linear algebra, so far ive just learnt there are these things called vector spaces and null spaces in R^n space

Answer 47

is a medal good enough haha

Answer 48

haha have you just stared it?

Answer 49

haha yes

Answer 50

oooo

Answer 51

loool. easy?

Answer 52

i learnt that a subspace you get with linear combinations of vectors of the matrix
and null spaces you get from X in Ax=b

Answer 53

its all been very joyful so far lmao

Answer 54

what about a basis for a subspace ;)

Answer 55

well it was mentioned

Answer 56

but more detail on that later later

Answer 57

i just heard him say the word by mistake lol

Answer 58

a basis is related to a dimension

Answer 59

i see

Answer 60

if u had a subspace which contained 3 vectors and one was a linear combination of the other then the basis of that subspace would be the 2 lin independent vectors

Answer 61

so dim=2

Answer 62

oh

Answer 63

interesting

Answer 64

pretty sweet tbh

Answer 65

so it would be a plane in some R^n?

Answer 66

oh i didn't specify if it was in R3 or RN...just giving a general case

Answer 67

if a basis 1 vector then a linear combination of that basis forms an infinity line passing through the ALL IMPORTANT BEAUTIFUL 0,0

Answer 68

origin point

Answer 69

lool. k from that info what would be the most simplest basis for r2?

Answer 70

this was stressed like some miraculous amazing point by the lecturer

Answer 71

a point

Answer 72

THE origin

Answer 73

[0,0]

Answer 74

lol wat no bahaha

Answer 75

what makes up the whole of R2? just with one vector

Answer 76

wait 2 vectors

Answer 77

oh okay