como realizar matriz 3x3 po gauss jordan

1. Gauss Jordan

2. 𝒙 −𝒚 +𝟐𝒛
−𝟑𝒙 +𝒚 +𝒛
𝟐𝒙 +𝟑𝒚 −𝒛
= 𝟖
= 𝟏
= −𝟗
Matriz Aumentada
𝟏 −𝟏 𝟐
−𝟑 𝟏 𝟏
𝟐 𝟑 −𝟏
𝟖
𝟏
−𝟗

3. Matriz Aumentada
𝟏 −𝟏 𝟐
−𝟑 𝟏 𝟏
𝟐 𝟑 −𝟏
𝟖
𝟏
−𝟗
Se debe convertir en matriz identidad
𝟏 𝟎 𝟎
𝟎 𝟏 𝟎
𝟎 𝟎 𝟏
𝒙
𝒚
𝒛
x y z r

4. 𝟏 −𝟏 𝟐
−𝟑 𝟏 𝟏
𝟐 𝟑 −𝟏
𝟖
𝟏
−𝟗
3R1+R2→ R2
(3x1)+(-3) = 3-3, (3*-1)+1 = -3+1, (3*2)+1 = 6+1, (3*8)+1 = 24+1
𝟏 −𝟏 𝟐
𝟎 −𝟐 𝟕
𝟐 𝟑 −𝟏
𝟖
𝟐𝟓
−𝟗 -2R1+R3→ R3
𝟏 −𝟏 𝟐
𝟎 −𝟐 𝟕
𝟎 𝟓 −𝟓
𝟖
𝟐𝟓
−𝟐𝟓
(-2*1)+2 = 2-2 , (-2*-1)+3 = 2+3, (-2*2)+(-1) = -4-1, (-2*8)+(-9) = -16-9

5. 𝟏 −𝟏 𝟐
𝟎 −𝟐 𝟕
𝟎 𝟓 −𝟓
𝟖
𝟐𝟓
−𝟐𝟓
−𝟏
𝟐R2→ R2
−𝟏
𝟐(0), −𝟏
𝟐(-2), −𝟏
𝟐(7), −𝟏
𝟐(25)
𝟏 −𝟏 𝟐
𝟎 𝟏 −𝟕/𝟐
𝟎 𝟓 −𝟓
𝟖
−𝟐𝟓/𝟐
−𝟐𝟓
R2+R1→ R1
0+1, 1+(-1), (-7/2)+2, (-25/2)+8
𝟏 𝟎 −𝟑/𝟐
𝟎 𝟏 −𝟕/𝟐
𝟎 𝟓 −𝟓
−𝟗/𝟐
−𝟐𝟓/𝟐
−𝟐𝟓

6. 𝟏 𝟎 −𝟑/𝟐
𝟎 𝟏 −𝟕/𝟐
𝟎 𝟓 −𝟓
−𝟗/𝟐
−𝟐𝟓/𝟐
−𝟐𝟓 -5R2+R3→ R3
(-5)(0)+0, ((-5)*1)+5, (-5)(-7/2)+(-5), (-5)(-25/2)+(-25)
𝟏 𝟎 −𝟑/𝟐
𝟎 𝟏 −𝟕/𝟐
𝟎 𝟎 𝟐𝟓/𝟐
−𝟗/𝟐
−𝟐𝟓/𝟐
𝟕𝟓/𝟐 2/25 R3→ R3
𝟏 𝟎 −𝟑/𝟐
𝟎 𝟏 −𝟕/𝟐
𝟎 𝟎 𝟏
−𝟗/𝟐
−𝟐𝟓/𝟐
𝟑
(2/25)(0), (2/25)(0), (2/25)(25/2), (2/25)(75/2)

7. 𝟏 𝟎 −𝟑/𝟐
𝟎 𝟏 −𝟕/𝟐
𝟎 𝟎 𝟏
−𝟗/𝟐
−𝟐𝟓/𝟐
𝟑
3/2 R3+R1→ R1
(2/3)(0)+1, (2/3)(0)+0, (3/2)(1)+(-3/2), (3/2)(3)+(-9/2)
𝟏 𝟎 𝟎
𝟎 𝟏 −𝟕/𝟐
𝟎 𝟎 𝟏
𝟎
−𝟐𝟓/𝟐
𝟑
7/2 R3+R2→ R2
(7/2)(0)+0, (7/2)(0)+1, (7/2)(1)+(-7/2), (7/2)(3)+(-25/2)
𝟏 𝟎 𝟎
𝟎 𝟏 𝟎
𝟎 𝟎 𝟏
𝟎
−𝟐
𝟑

8. 𝟏 𝟎 𝟎
𝟎 𝟏 𝟎
𝟎 𝟎 𝟏
𝟎
−𝟐
𝟑
𝒙 −𝒚 +𝟐𝒛
−𝟑𝒙 +𝒚 +𝒛
𝟐𝒙 +𝟑𝒚 −𝒛
= 𝟖
= 𝟏
= −𝟗
0-(-2)+2(3)=8
2+6=8
8=8
-3(0)+(-2)+3=1
-2+3=1
1=1
2(0)+3(-2)-(3)=-9
-6-3=-9
-9=-9