How do you solve $5 x - 5 y + 10 z = - 11$ $5x - 5y + 10z = -11$ , $10 x + 5 y - 5 z = 1$ $10x + 5y - 5z = 1$ and $15 x - 15 y - 10 z = - 1$ $15x - 15y -10z = -1$ using matrices?

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Answer 1 · 2018-08-02T07:22:27

The solution is $((x),(y),(z))=((-2/5),(1/5),(-4/5))$

Perform the Gauss-Jordan Elimination on the augmented matrix

$A=((5,-5,10,|,-11),(10,5,-5,|,1),(15,-15,-10,|,-1))$

Make the pivot in the first column and first row

$R1larr((R1)/5)$

$((1,-1,2,|,-2.2),(10,5,-5,|,1),(15,-15,-10,|,-1))$

Eliminate the first column

$R2larr(R2-10R1)$ and $R3larr(R3-15R1)$

$((1,-1,2,|,-2.2),(0,15,-25,|,23),(0,0,-40,|,32))$

Make the pivot in the second column and second row

$R2larr((R2)/15)$

$((1,-1,2,|,-2.2),(0,1,-5/3,|,23/15),(0,0,-40,|,32))$

Eliminate the second column

$R1larr(R1+R2)$

$((1,0,1/3,|,-2/3),(0,1,-5/3,|,23/15),(0,0,-40,|,32))$

Make the pivot in the third column and third row

$R3larr((R3)/-40)$

$((1,0,1/3,|,-2/3),(0,1,-5/3,|,23/15),(0,0,1,|,-4/5))$

Eliminate the third column

$R1larr(R1-1/3R3)$ , and $R2larr(R2+5/3R3)$ ,

$((1,0,0,|,-2/5),(0,1,0,|,1/5),(0,0,1,|,-4/5))$

The solution is

$((x),(y),(z))=((-2/5),(1/5),(-4/5))$

How do you solve 5x - 5y + 10z = -115x−5y+10z=−115x - 5y + 10z = -11, 10x + 5y - 5z = 110x+5y−5z=110x + 5y - 5z = 1 and 15x - 15y -10z = -115x−15y−10z=−115x - 15y -10z = -1 using matrices?