Question

solve gauss elimination

(1) w-x+3y-3z=3 (2) 3x1+2x2+x3=3
2w-3x+y-11z=1 2x1+x2+x3=0
5w-2x+5y-4z=5 6x1+2x2+4x3=6
3w+4x-7y+2z=-7

Answer 1

Answer on Question #58274 – Math – Linear Algebra

Question

Solve gauss elimination

1. w-x+3y-3z=3

2. 2w-3x+y-11z=1

3. 5w-2x+5y-4z=5

4. 3w+4x-7y+2z=-7

Solution

w-x+3y-3z=3 (1)

2w-3x+y-11z=1 (2)

5w-2x+5y-4z=5 (3)

3w+4x-7y+2z=-7 (4)

w-x+3y-3z=3 (1)

-x-5y-5z=-5 (2)-2×(1)

3x-10y+11z=-10 (3)-5×(1)=(3)*

7x-16y+11z=-16 (4)-3×(1)=(4)*

w-x+3y-3z=3 (1)

x+5y+5z=5 2×(1)-(2)=(2)*

3x-10y+11z=-10 (3)-5×(1)=(3)*

7x-16y+11z=-16 (4)-3×(1)=(4)*

w-x+3y-3z=3 (1)

x+5y+5z=5 2×(1)-(2)=(2)*

-25y-4z=-25 (3)*-3×(2)*

-51y-24z=-51 (4)*-7×(2)*=(4)~

w-x+3y-3z=3 (1)

x+5y+5z=5 (2)*

y+4/25z=1 ((3)*-3×(2)*)/(-25)=(3)~

(-24+51×4/25)z=0 (4)~+51×(3)~

```latex

$\begin{array}{l} \mathrm{z = 0} \\ \mathrm{y = 1} \\ \mathrm{x + 5 = 5} \\ \mathrm{w - x + 3 = 3} \end{array}$

$\begin{array}{l} \mathrm{z = 0} \\ \mathrm{y = 1} \\ \mathrm{x = 0} \\ \mathrm{w = 0} \end{array}$

Answer: $z = 0, y = 1, x = 0, w = 0$ .

Question

Solve gauss elimination

2. $\begin{cases} 3x1 + 2x2 + x3 = 3 \\ 2x1 + x2 + x3 = 0 \\ 6x1 + 2x2 + 4x3 = 6 \end{cases}$

Solution

3x1+2x2+x3=3 (1)

2x1+x2+x3=0 (2)

6x1+2x2+4x3=6 (3)

3x1+2x2+x3=3 (1)

x1+x2=3 (1)-(2)=(2)*

-6x1-6x2=-6 (3)-4×(1)=(3)*

3x1+2x2+x3=3 (1)

X1+x2=3 (2)*

0=12 (3)*+6×(2)*

System doesn't have solution because $0 \neq 12$ (it means that there are no $x1, x2, x3$ which yield $0 = 12$ ).

Answer: no solution.

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