Determine the value of (1 + xyz)

**zorro** · November 1st 2009, 10:52 PM

Question : If x, y, z are all different and given that
$ \begin{vmatrix} x & x^2 & 1 + x^3 \\ y & y^2 & 1 + y^3 \\ z & z^2 & 1 + z^3 \end{vmatrix} = 0, $

Determine the value of (1 + xyz)

**Jodles** · November 1st 2009, 11:09 PM

What have you done, and where are you stuck?

**math2009** · November 1st 2009, 11:16 PM

$\det\begin{bmatrix} x&x^2&1+x^3\\ y&y^2&1+y^3\\ z&z^2&1+z^3 \end{bmatrix}=\cdots=(z-x)(z-y)(y-x)(1+xyz)=0$ , if you have enough patience.

$\because x\neq y\neq z\neq x \ \therefore 1+xyz=0$

**mr fantastic** · November 2nd 2009, 02:50 PM

Also asked and replied to here: http://www.mathhelpforum.com/math-he...terminant.html

**zorro** · December 1st 2009, 12:29 PM

Originally Posted by mr fantastic

Also asked and replied to here: http://www.mathhelpforum.com/math-he...terminant.html

I have seen the reply post in the other thread but cold u please provide me with the end answer, just to be sure that i have done it right or no.At present i am trying to do as provided by the prev thread but it would be good if u could provide with the end result
ie, $(1 + xyz)$

**mr fantastic** · December 2nd 2009, 12:38 AM

Originally Posted by zorro

I have seen the reply post in the other thread but cold u please provide me with the end answer, just to be sure that i have done it right or no.At present i am trying to do as provided by the prev thread but it would be good if u could provide with the end result
ie, $(1 + xyz)$

You need to start showing some effort here. Post all your work. Say where you get stuck.

**zorro** · December 22nd 2009, 04:45 PM

Originally Posted by mr fantastic

You need to start showing some effort here. Post all your work. Say where you get stuck.

After doing the determinant i am getting the following please advice if correct or no

$(xy^2 - xz^2 - yx^2 + zx^2 + yz^2 - zy^2)(1+xyz)=0$

$\therefore (1+xyz) = 0$

**mr fantastic** · December 23rd 2009, 01:15 AM

Originally Posted by zorro

After doing the determinant i am getting the following please advice if correct or no

$(xy^2 - xz^2 - yx^2 + zx^2 + yz^2 - zy^2)(1+xyz)=0$

$\therefore (1+xyz) = 0$

Post #3 already confirms your answer.

**zorro** · December 23rd 2009, 01:17 AM

Originally Posted by mr fantastic

Post #3 already confirms your answer.

Just wanted to check i did it correctly or no .........want to know if the step is correct or no?????

**mr fantastic** · December 23rd 2009, 01:27 AM

Originally Posted by zorro

Just wanted to check i did it correctly or no .........want to know if the step is correct or no?????

Look at post #3 and compare answers. Does $(xy^2 - xz^2 - yx^2 + zx^2 + yz^2 - zy^2)$ (which is what you have) equal $(z-x)(z-y)(y-x)$ ? (the answer in post #3 is correct, by the way).

**simplependulum** · December 25th 2009, 06:23 PM

Originally Posted by zorro

After doing the determinant i am getting the following please advice if correct or no

$(xy^2 - xz^2 - yx^2 + zx^2 + yz^2 - zy^2)(1+xyz)=0$

$\therefore (1+xyz) = 0$

I think some marks will be deducted in your solution .

You should mention that iff two of the elements are the same , the factor

$xy^2 - xz^2 - yx^2 + zx^2 + yz^2 - zy^2 = 0$

because you have only showed that

$xy^2 - xz^2 - yx^2 + zx^2 + yz^2 - zy^2 = 0$

OR

$1 + xyz = 0$

so $1 + xyz$ is not 100% zero

Factorising it you will get full mark !

Thread: Determine the value of (1 + xyz)

LinkBack

Thread Tools

Display

Determine the value of (1 + xyz)

Could u please provide the end result

Is this correct?

Similar Math Help Forum Discussions

determine the value of a

Determine whether the series converges, and if it converges, determine its value.

Determine whether these sets S are bounded, and determine sup(S) and inf(S) if they e

Determine a Dif EQ

Determine the value of a

Search Tags