October 24th, 2014, 09:19 AM  #1 
Newbie Joined: Oct 2014 From: Lithuania Posts: 4 Thanks: 0  determinant
Can someone help me to solve this determinant? I have no idea how to start... залить картинку thanks for the help!! Last edited by robertson; October 24th, 2014 at 09:34 AM. 
October 24th, 2014, 09:47 AM  #2 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,000 Thanks: 132 Math Focus: Trigonometry 
Zero? All columns contain zero, right?

October 24th, 2014, 09:53 AM  #3 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 750 Math Focus: Wibbly wobbly timeywimey stuff.  But $\displaystyle \left  \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right  = 1$ and there is a 0 in every column. It has to be all zeros in at least one column or all zeros in at least one row to give a determinant of zero. Dan 
October 24th, 2014, 10:24 AM  #4 
Newbie Joined: Oct 2014 From: Lithuania Posts: 4 Thanks: 0 
I guess, to solve this determinant we need to extract (don't know if it's the right word) by first row and column. Or something like that. What do You think?

October 24th, 2014, 10:51 AM  #5 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 750 Math Focus: Wibbly wobbly timeywimey stuff.  
October 24th, 2014, 01:09 PM  #6 
Newbie Joined: Oct 2014 From: Lithuania Posts: 4 Thanks: 0 
hmmm .... nop, I'm not so good at this one... Doesn't work :/

October 24th, 2014, 02:05 PM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 750 Math Focus: Wibbly wobbly timeywimey stuff. 
Try a couple of simple cases: $\displaystyle Det \left [ \begin{matrix} a & b & c \\ x & x & 0 \\ 0 & x & x \end{matrix} \right ] = a \left  \begin{matrix} x & 0 \\ x & x \end{matrix} \right   b \left  \begin{matrix} x & 0 \\ 0 & x \end{matrix} \right  + c \left  \begin{matrix} x & x \\ 0 & x \end{matrix} \right $ $\displaystyle = a ( x^2 )  b ( x^2 ) + c (x^2 ) = (a + b + c)x^2$ Try the 4 x 4 yourself. There's an obvious pattern that emerges. Post your the work of your 4 x 4 and we'll take a look at it. Dan 
October 25th, 2014, 12:49 AM  #8 
Newbie Joined: Oct 2014 From: Lithuania Posts: 4 Thanks: 0  
October 25th, 2014, 10:05 PM  #9  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 750 Math Focus: Wibbly wobbly timeywimey stuff.  Quote: I had originally thought to give you the idea of expanding out by the second row, not the first, and I forgot to do so. I apologize. That's the only simple way to spot a useful pattern. (Well, you can do it the way I presented it, but it's harder.) Dan  

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