Question

find a basis for the null space of A (see attachment)

Answer 1

\[\left[\begin{matrix}1 & -1 &3 \\ 5 & -4 & -4\\7 &-6 &2\end{matrix}\right]\]

Answer 2

@camoJAX this time, it's me. help, please

Answer 3

trying to see now

Answer 4

taking longer than i thought, still going though

Answer 5

First find it's row reduced echelon form.

Answer 6

yep and you'll get \[1x _{1}-1x _{2}+3x _{3}=0\]
\[1x _{2}-19x _{3}=0\]
still working though

Answer 7

yes, I got it as \[\left[\begin{matrix}1 & -1 &3 \\ 0 & 1 & -19\\0 & 0 & 0\end{matrix}\right]\]

Answer 8

bottom row will be all zeros

Answer 9

@camoJAX bingo.

Answer 10

how to make matrices on here?

Answer 11

stack -22,19, 1 on each other and thats the answer

Answer 12

go to equation right below this box. you can see many symbol, choose matrix symbol, you will have something like ? ? .. whenever see? put the number there and & ? put number at ? if you need 3 terms add 1 & symbol and then type the number there. if you want to take 1 more row, \\ and repeat

Answer 13

To make a matrix type:
\begin{bmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{bmatrix}

You use & to delimit columns and \\ to delimit rows.

Answer 14

@camoJAX 16 not 22

Answer 15

\[\left(\begin{matrix}16 \\ 19\\1\end{matrix}\right)\]

Answer 16

my question starts from now on. I got it but is it the null space or we have to break it down to 3 vectors as

Answer 17

You have one free variable, so your null space is just one column

Answer 18

yep dont know why i was thinking negative plus a negative and made the 19 positive then subtracted it from -3. my bad

Answer 19

\[\left(\begin{matrix}16 \\ 0\\0\end{matrix}\right)\left(\begin{matrix}0 \\ 19\\0\end{matrix}\right)\left(\begin{matrix}0 \\ 0\\0\end{matrix}\right)\]

Answer 20

\[
x_1 = x_2 - 3x_3 = 19x_3-3x_3=16x_3 \\
x_2 = 19x_3
\]

Answer 21

meant neg x neg lol

Answer 22

thanks a lot both friends. so, since I have 1 free variable, 1 column basis in null space. if I have 2 , 2 columns basis. is it correct?

Answer 23

Yes, one column per free variable.

Answer 24

agree

Answer 25

thank you very much. "The power of cooperation"

Answer 26

@camoJAX which class do you have now?

Answer 27

i'm still on Cal homework right now

Answer 28

cal3? which school?

Answer 29

yea Cal 3, Lamar Univ..kinda little,not too big school in TX

Answer 30

still better than me, I am in community college.

Answer 31

I am struggling with 3 math courses this semester. I have cal3, linear algebra and discrete

Answer 32

that doesn't mean anything just depends what you do with your knowledge

Answer 33

i'm taking those too except discrete

Answer 34

my discrete is level 2, too many things to do. terrible

Answer 35

i never heard of discrete but just looked it up and I pity you bro (...or sis) lol

Answer 36

sister. no choice for me. my major is math. how can I avoid math courses?

Answer 37

what is your major?

Answer 38

true, sometimes math can be difficult but I love it when I'm able to solve a problem.

Answer 39

Civil Engineering

Answer 40

Lol. not lesser than me in math. for sure

Answer 41

ok, being fan each other to get help whenever we need, deal?

Answer 42

definite deal

Answer 43

hey , my pro gives me a challenge question, deal after spring break, you can take a look and if you have time, think about helping me. i didn't have the solution yet. the problem is : why the procedure to get transition matrix from B to B' work. show your proof.

Answer 44

it means P from B-->B' is |B'|B|----> | I | P from B -->B'|. why it works.

Answer 45

the question is due after the break?
your break is March11-15?

Answer 46

no need to press yourself. It is just extra credit, i don't need it that much. my break from 3 to 10. I am during break time. if not, how can i have time to play here

Answer 47

ohh you're on break now. I thought you probably just got on this site whenever. thats what i do

Answer 48

i wanna know the answer now, i'll be thinking about it though

Answer 49

too bad. I asked, pointed at particular people who has smartscore at top 99 -100 all of them say " sorry, I cannot help" or "sorry,it 's not my strong".

Answer 50

i can ask my prof if I never figure it out

Answer 51

ok. it's too late, I have to go to bed now. nice to meet you. whenever you got it, send me message.

Answer 52

cool, night. nice to meet you also

Answer 53

bye bye