hey im stuck on gauss-jordan questions and wud really appreciate if someone could help me!?

Question

{5 -1 -1 -8 : 5 }
{10 -2 4 2 : 8}


and the second one is :

{ 1 -2 1 -4 : -3}
{ 1 3 7 2 : 18}
{ 1 -12 -11 -16 : -37}


thanks a million!!! Im sooo stuck :(

and if someone instead of calling me lazy would like to actually explain how to do it either, i would appreciate it.

i just get to a point and dnt know how to go further..this is what ive done in both so far :

heres 1:

{5 -1 -1 -8 : 5}
{10 -2 4 2 :8}

this is what ive done so far..

{1 -1/5 -1/5 -8/5 :1}
{-5 1 -2 -1 :-4}

{1 -1/5 -1/5 -8/5 :1}
{0 0 -3 -9 : 1}

{1 1 1 8 :-5}
{0 0 -3 -9 :1 }



and the second one is :

{1 -2 1 -4 :-3}
{1 3 7 2 :18}
{1 -12 -11 -16 : -37}

this is what ive got so far...

{1 -2 1 -4 :-3}
{0 5 6 6 :21}
{0 -10 -12 -12 : -34}


{1 -2 1 -4 : -3}
{0 1 6/5 6/5 :21/5}
{0 5 6 6 : 17}


{1 -2 1 -4 :-3}
{0 1 6/5 6/5 :21/5}
{0 0 0 0 : -4)

{1 -2 1 -4 :-3}
{0 1 0 6 :39/5}
{0 0 0 0: -4}
id really apprciate someone telling if im completely wrong in where im going, or what im suposed to do please :(

Answer 1

What is it you don't understand about the G-J method?

In your first one, you were perfect up to
(1 -1/5 -1/5 -8/5 : 1)
(0 0 -3 -9 :1),
but in your next matrix, you cannot only multiple the second through the last element by -5, you Must treat Every element the same. Consequently, you don't want to manipulate the first row any further, because that would destroy the desirable 1 in the 1,1 position. Operate on the second row by getting a 1 in the 2,3 position; then add 1/5 times the second row to the first--the result will be your row reduced echelon form.

In your second one, you were okay up to your second to the last matrix, but your last is wrong. (I have no idea what you did.) What you should do next is add 2 times the second row to the first row; that will put a zero above the desirable 1 in the 2,2 position. OR you might notice that the third row in your nexr to the last equation tells you this system has no solution. The row (0 0 0 0 : -4) stands for the equation 0x + 0y + 0u + 0v = -4, which of course is impossible.

Good luck.