help with 3x3 matrix

[luken93]

Firstly someone needs to explain to me how to do matrix on latex
Secondly,

If A=
       
       

Find and hence find

I've found but having a bit of trouble with the inverse

Thanks

[m@tty]

I didn't do CAS, so I don't know what you know. But any matrix that has a row consisting of only zeros, has a determinant of zero, and hence has no inverse.

Also, to show a matrix:

Code: [Select]

\begin{bmatrix} 2&0&0 \\ 0&0&2 \\0&0&0\end{bmatrix}
That is, begin with \begin{bmatrix} then enter each element of the first row, separated by '&', when you get to the end of the row insert '\\' and repeat completing each row until you finish the matrix. When you get to the very end place \end{bmatrix}.

[luken93]

ok thanks, just realised i made an error

A=, not

A=

now can you redo the question haha

[m@tty]

Well thanks :buck2:





I didn't do CAS, so I don't know what you know. But any matrix that has a row consisting of only zeros, has a determinant of zero, and hence has no inverse. <-Irrelevant now.

Well yeah, I still don't know what you know. What have you been told about determinants/square matrices/power matrices?..

[luken93]

aah not much, i know how to get inverse of 2x2 but im not really sure how to do it for a 3x3

i looked in the solutions pdf from here and they show that you set up



hence



therefore

but somehow they get that a=2, whereas i thought it was 4?

[m@tty]

Ok so:



and all other elements are equal to zero.




where is the 3x3 identity matrix.

Is this how you are meant to deduce it?

[luken93]

aah ok i get it now, just wasn't looking at the 4a 4c 4b etc = a properly, i was thinking that it shudve been 4, 0, 0

couldve solved it ages ago hahaha

[luken93]

next test: UniMelb Maths Comp

[tram]

i'm pretty sure that 3x3 matricies are not part of the study design or mm cas, only 2x2. They're just there if you're interested. You don't even reli have and pure matricies questions anyway-i've never come across one. You only use matricies for probablility.

And even if 3x3 matricies were on the course, i'm postive you would've had to find inverses, the only way of doing that is with uni maths techniques

However matracies are soooo cool once you learn more about them. Uni maths is awesome for taking all this kinda stuff further and making maths interesting. Pretty sure m@tty would agree with me.

[kyzoo]

And even if 3x3 matricies were on the course, i'm postive you would've had to find inverses, the only way of doing that is with uni maths techniques

However matracies are soooo cool once you learn more about them. Uni maths is awesome for taking all this kinda stuff further and making maths interesting. Pretty sure m@tty would agree with me.

Uni Maths Matrices is the most annoying thing >.<. If you screw up the arithmetic just once, then you have to start over again. Finding the inverse of a 3x3 matrix take likes...30-40 arithmetic operations =/

[tram]

^definitely, lol, caculators make it sooooo much easier. But if you do it the right way, you usually only need like....~15 steps. But yea....defs, one TINY mistake at the start means you're screwed

[luken93]

it was only 1 question in matrices chapter extended response, just wanted to know how to do it just incase our teacher sprung it on us.

[kyzoo]

^definitely, lol, caculators make it sooooo much easier. But if you do it the right way, you usually only need like....~15 steps. But yea....defs, one TINY mistake at the start means you're screwed

Too bad we aren't allowed to use calculators for final exam =(

[m@tty]

You aren't allowed calculators? Not even a scientific?

[kyzoo]

Directly quoted from the book

You will NOT be allowed to bring any of the following into your 620-190 examinations in November, nor will you be provided with them

~ A calculator (of any kind)
~ Any form of notes or summary ('cheat') sheet
~ A formula sheet