Solving simultaneous equations with matrix

[saranga]

i don't understand how to get second box using first box in the picthure that has attached.could someone help me?

 

[Simon Bridge]

The matrix has a column of zeros ... look through your notes to find out what that means.

The 1st box gives equations:
$0x_1 + x_2 + 4x_3 = 0$
$0x_1 -x_2 + 6x_3 = 0$

The second box gives the rather weird construction:
$$\frac{x_1}{6+4}=\frac{x_2}{0-0} = \frac{x_3}{0-0}$$

... it looks like it is trying to show you something about a technique already used before.
I wouldn't do it that way. I'd just solve the simultaneous equations.

 

[Mark44]

The second box gives the rather weird construction

I agree. To me it makes more sense to continure with row reduction, not stop in the middle.
$\begin{bmatrix} 0 & 1 & 4 \\ 0 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \equiv \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0\end{bmatrix}$
I've skipped a couple of steps here.
That last matrix represents this system:
$x_2 = 0$
$x_3 = 0$
$x_1$ doesn't appear, which means it is arbitrary, all possible eigenvectors are $k \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$

 

[saranga]

thanks pal

The matrix has a column of zeros ... look through your notes to find out what that means.

The 1st box gives equations:
$0x_1 + x_2 + 4x_3 = 0$
$0x_1 -x_2 + 6x_3 = 0$

The second box gives the rather weird construction:
$$\frac{x_1}{6+4}=\frac{x_2}{0-0} = \frac{x_3}{0-0}$$

... it looks like it is trying to show you something about a technique already used before.
I wouldn't do it that way. I'd just solve the simultaneous equations.

 

[saranga]

I agree. To me it makes more sense to continure with row reduction, not stop in the middle.
$\begin{bmatrix} 0 & 1 & 4 \\ 0 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \equiv \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0\end{bmatrix}$
I've skipped a couple of steps here.
That last matrix represents this system:
$x_2 = 0$
$x_3 = 0$
$x_1$ doesn't appear, which means it is arbitrary, all possible eigenvectors are $k \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$

ok thanks for your idea pal

 

[Simon Bridge]

For future reference, a note on English language useage in USA and anywhere in the UK Commonwealth or the former British Empire: the construction "thanks... pal" is usually taken as sarcasm.
Since these forums attract an international audience, and so many people are writing with English as their second or later language, and from vastly different cultures, we are forced to take such statements at face value much of the time... so no offence is taken. It can, however, lead to ambiguous communication. If you intend to communicate gratitude and friendship then fine - if you mean that the answers are, in some way, unsatisfactory - then you need to elaborate.

 

[Stephen Tashi]

From my (USA) point of view "thanks pal" isn't offensive or sarcastic. However, it is anachronistic - it sounds like common speech from from 1940's. Someone can probably cite a film where Humphrey Bogart says it.

 

[Mark44]

From my (USA) point of view "thanks pal" isn't offensive or sarcastic. However, it is anachronistic - it sounds like common speech from from 1940's. Someone can probably cite a film where Humphrey Bogart says it.

I agree. I also don't believe @saranga's intent was to be sarcastic.

 

[Simon Bridge]

It's not "pal" by itself that denotes sarcasm - it's the construct and context that makes it ambiguous, but I may be being too sensitive here - so nobody has ever heard "thanks pal" sarcastically? Maybe that has fallen out of use too?

Don't get me wrong, it can be OK here too ... you need the intonation to tell the difference and the anachronism in writing it down can primes the reader to question the intent. My point is not that I thought the intent was sarcastic but that I could not tell... especially as the question we all answered was not strictly the one asked.
If you don't understand the way the book does it then do it another way that you do understand... oh gee, thanks pal, I didn't think of that already...
These things can change, maybe I'm out of date? - is "with all due respect" still OK in the US?

 

[Mark44]

It's not "pal" by itself that denotes sarcasm - it's the construct and context that makes it ambiguous, but I may be being too sensitive here - so nobody has ever heard "thanks pal" sarcastically? Maybe that has fallen out of use too?

Don't get me wrong, it can be OK here too ... you need the intonation to tell the difference and the anachronism in writing it down can primes the reader to question the intent. My point is not that I thought the intent was sarcastic but that I could not tell... especially as the question we all answered was not strictly the one asked.
If you don't understand the way the book does it then do it another way that you do understand... oh gee, thanks pal, I didn't think of that already...
These things can change, maybe I'm out of date? - is "with all due respect" still OK in the US?

"With all due respect" is fine. Based on the IP address, the OP is posting from Asia, so I really don't believe there was any sarcastic intent. Can we drop this now?