Álgebra Lineal actividad

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4x-6y+2z=4 3x-10x=5-16

X+ y + z=4 -7x=-11 [pic 58]

5 + z =8 x=11 3+y+5=3

5x+z=8 7 Y =3-1.5-0.5[pic 59]

z =8-5x [pic 60][pic 61]

x + y = 4[pic 62]

4) x – y = 2

[pic 63]

X+y꞊4

X -y꞊2

2x ꞊6[pic 64]

2 x ꞊6[pic 65][pic 66][pic 67]

2 2

X ꞊3

Sustituyo

X+y꞊4

3+y꞊4

3+3+y꞊4-3[pic 68][pic 69]

y꞊1

4x + 2y – 3z = 8[pic 70]

5) 2x – 3y + z = 6

- x + 4y +2z = 5

2x-3y+z=6 z=21-5x

X+4y+z=5 z=21-5(4.4)[pic 71]

3x +2z=11 z=21-22

Z꞊-1

4x+4y-6z=16

1x+4y- z =5 4.4+y=8[pic 72]

5x 7=21 y꞊2.6

5x+z=21

Z=21-5x

3x+2(21-5x)=11

3x+ 42-10x =11

3x-10x=11-42

-7x=-31

=31

7

x꞊4.4

[pic 73]

-5x + y –3 z = 3 (1)

6) x – 3y +6z = 2 (2)

2x + 4y + 4z = 4 (3)

-5 1 -3 ꞊ (60-12+12)-(4-120+18)[pic 74][pic 75][pic 76][pic 77][pic 78][pic 79]

1 -3 -6 ꞊60+98[pic 80][pic 81]

2 4 4 ꞊158[pic 82][pic 83][pic 84]

-5 1 -3

1 -3 -6

[pic 85][pic 86][pic 87]

3 1 -3 x꞊(-36-24+24)-(8+72+36)[pic 88]

2 -3 6 158[pic 89][pic 90]

4 4 4[pic 91][pic 92]

3 1 -3 76

X꞊ 2 -3 6 x꞊-152[pic 93]

158[pic 94][pic 95][pic 96]

79

X꞊-76

79[pic 97]

[pic 98][pic 99]

5 3 -3 y꞊ (40-12+36)-(12+120-12)[pic 100][pic 101]

1 2 6 158[pic 102][pic 103][pic 104]

2 4 4[pic 105][pic 106]

5 3 -3 y꞊64-120

Y ꞊ 1 2 6 158[pic 107]

[pic 108][pic 109]

y꞊28 79

Sustituyo en ec. 3

2x+4y+4z꞊4

2 (-76)+4(-28)+4z꞊4

79 79[pic 110][pic 111]

-152 – 112 + 4z꞊4

79 79[pic 112][pic 113]

264-264+4z꞊4+264[pic 114]

79 79 79 4z꞊580[pic 115][pic 116][pic 117]

79

4z꞊580 4

79 [pic 118]

145

290[pic 119]

z꞊ 580[pic 120][pic 121]

316[pic 122]

158[pic 123]

79

[pic 124]

z꞊145 79

7) x + y =3[pic 125]

x – y = 1

X+ y ꞊3[pic 126]

x- y ꞊1[pic 127]

2x ꞊4

2x ꞊4[pic 128]

2 2[pic 129]

x꞊2

Sustituyo

X+y꞊3

2+y꞊3

2-2+y꞊3-2[pic 130][pic 131]

y꞊1

8) 2x +2 y = 3[pic 132]

3x + 4y = 1

Multiplico ec.1 por (-3) y ec.2 por (2)

-3(2x+2y꞊3)

2(3x+4y꞊1

-6 x -6y꞊-9

6 x+8y꞊2

2y꞊-7

2y꞊-7 /2[pic 133]

2[pic 134]

y꞊7/ 2

Sustituyo y en ec. 2

3x+4y꞊1

3x+4(-7/2) ꞊1

3x-14꞊1

3x-14+14꞊1-14[pic 135][pic 136]