Question

i cant seem to solve this question

Answer 1

L stands for lower triangular
U for upper triangular

Answer 2

so than should it be the last option? number 4?

Answer 3

option 2 and 4 both are in the correct form, but when you multiply them one of them is the answer

Answer 4

im not sure how to do this,,,,,

Answer 5

do you want to know how to factor it or how to find out the answer ?

Answer 6

since you're given options, simply multiplying a row in L by the matrix U gives you the answer fast. lets try 2nd option :

\[\large \left[\begin{matrix}1&0&0&0\end{matrix}\right] \left[\begin{matrix}3&-2&-4&0\\0&1/3&2/3&0\\0&0&1&0\\0&0&0&-1\end{matrix}\right] = \left[\begin{matrix}3&-2&-4&0\end{matrix}\right] \]

which is exactly same as the coefficients of your first equation, yes ?

Answer 7

yes, they are, what does that mean?

Answer 8

that means 2nd option is most likely the answer
however you need to work the other two rows also to be fully sure

Answer 9

Note that @perl eliminated options 1 and 3 earlier because they don't fit L/U definitions

Answer 10

basically you're factoring the `coefficient matrix` of given system of equations as LU :
\[\large A = LU\]

Answer 11

sorry i havent studdied this part yet, dont know

Answer 12

this is very important part before you start subspces and other advanced stuff

Answer 13

its also called LU factorization

Answer 14

yeah have to study this...

Answer 15

btw all you need to know to do LU factorization is `gauss jordan elimination` and finding inverse

Answer 16

yeah i have been trying to go through the excersies in order, so havent got up to this part yet

Answer 17

watch this video when free
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-4-factorization-into-a-lu/

Answer 18

thanks!