Matrices

[VAISHU]

Dear all,

kindly help me to solve the question has per the attachment.
Due to I can't solve it after so many times have tried.

Navi

[Guest]

Look at this tool:

http://www.math10.com/scripts/matrices/ ... ators.html

[leesajohnson]

It's difficult to solve here because it's too long to solve as well as it requires table form so that is not possible. I will upload a pic of solution after some time.

[HallsofIvy]

i have no idea what "table form" is but this looks relatively easy to solve. "Table form" may refer to "matrices" but "Gaussian elimination" does not require matrices.

The first thing I notice is that the third equation does not involve [tex]x_3[/tex] so I would start by eliminating it from equations one and two. Multiply the first equation by 7:
[tex]7x_1- 28x_2+ 7x_3= 0[/tex] and subtract [tex]2x_1- 3x_2+ 7x_3= 0[/tex] to get [tex]5x_1- 25x_2= 0[/tex].

Now we have [tex]5x_1- 25x_2= 0[/tex] and [tex]x_1- 2x_2= 0[/tex]. Dividing the first of those equations by 5, [tex]x_1- 5x_2= 0[/tex]. Subtract the other equation from that to get [tex]3x_2= 0[/tex] so [tex]x_2= 0[/tex]. Then [tex]x_1- 5x_2= x_1= 0[/tex] and finally [tex]x_1- 4x_2+ x_3= 0- 0+ x_3= 0[/tex].

That really should have been obvious from the first since every equation is "= 0". Clearly [tex]x_1= x_2= x_3= 0[/tex] satisfies the equations and, unless the equations are "dependent", which is not the case here, that is the only solution.

By the way, this problem has nothing to do with "Progressions, Series". It should have been posted under "Simultaneous Equations, Systems of Equations/Inequalities".