Assignment [MatS-9-XX1-K06]

Einsendeaufgabe : Lineare Gleichungssysteme. MatheS9 – XX1: K06

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Mathematics
MatS-9-XX1-K06

University, School

ILS Institut für Lernsysteme - Fernhochschule Hamburg

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Einsendeaufgabe : Lineare Gleichungssysteme. MatheS9 – XX1: K06

MatheS9 – XX1 - K06


1.

a) I: 3x + 4y = 1 |- 3x

4y = 1 – 3x |:2


2y = ½ – 3/2 x


II: 5x = 2y – 7 |+7


5x + 7 = 2y


=> ½ - 3/2 x = 5x + 7 | + 3/2 x

½ = 13/2 x +7 | - 7

- 13/2 = 13/2 x | mal 2/13


- 1 = x


I: 3 mal -1 + 4 y = 1

- 3 + 4 y = 1 | + 3

4y = 4 | : 4

y = 1

Probe: 3 mal -1 + 4 mal 1 = 1

-3 +4 = 1

1 = 1 L{-1; 1}


b)

I: ¼ x – 3/20 y = ½ |mal – 3/2

- 3/8 x +9/40 y = - ¾ |- 9/40 y


- 3/8 x = -3/4 – 9/40 y

II: - 3/8 x + 4/5 y = 5 | - 4/5 y


- 3/8 x = 5 – 4/5 y


=> -3/4 – 9/40 y = 5 – 4/5 y | + 4/5 y = 32/40 y

- ¾ + 23/40 y = 5 | + ¾

23/40 y = 23/4 | mal 40/23


y = 23/4 mal 40/23 = 40/4 = 10 = y


I: 1/4x – 30/20 = ½ | + 3/2

¼ x= 2 | mal 4


x = 8 L (8; 10)


2.

a) I: 9 – x = 3y |: 3


3 – 1/3 x = y


=> in II: 2 (3 – 1/3 x) + 2x = 2

6 – 2/3 x + 2x = 2 | - 6

4/3 x = - 4 | mal ¾

x = - 3

.....[read full text]

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12 = 3+ | : 3


4 = + 7 { 3; 4 }


+) 1: 1/3≠ + 2/7 + = 6

11: 3+ – 7≠ = 0 | +7≠

3+ = 7≠ | : 3

+ = 7/3 ≠


1: 1/3≠ + 2/7∋∋†7/3 ≠= 6

1/3≠ + 2/3≠ = 6


≠= 6

11: 3+ -(7∋∋†6) = 0 | +42

3+= 42 | : 3


+ = 14 7 {6;14}

3.

∋) 1: 15≠ – 17+ = 11 |∋∋†4

11: 25≠ + 4+ = 83 ∋∋† 17


60 ≠ – 68+ = 44

425≠ + 68+ = 1411

485 ≠ = 1455 | : 485

≠ = 3

15∋∋† 3 – 17+ = 11 | - 45

- 17+ = - 34 | : - 17

+ = 2 7 { 3; 2 }


+) 1/7≠ – 3/4+ = 16 |∋∋† 7 11 - 3/14≠ + 1/5+ = - 5,5 | ∋∋† 14/3

≠ – 21/4 += 112 - ≠ + 14/15 + = - 77/3


=&⊥†; ≠ – 21/4 + = 112

-≠ + 14/15 + = - 77/3

- 315/60 + = 112 = 336/3

56/60 + = - 77/3

- 259/60 + = 259/3 | ∋∋† – 60/259

+ = - 20


1/7 ≠ – (¾ ∋∋† – 20) = 16

1/7 ≠ – (¾ ∋∋† - 20 = 16

1/7 ≠ +15 = 16 | - 15

1/7≠ = 1 | ∋∋† 7

≠ = 7 7 { 7; - 20}

4.

∋) 1: ≠ + + = 38

11: 4≠ – 12 = 3+ | - 4≠

- 12 = 3+ – 4≠ | + 50


38 = 3+ – 4≠ - +50

=&⊥†; ≠ + + = 3+ – 4≠ + 50 | + 4≠

5≠ + + = 3+ + 50 | - +

5≠ = 2+ + 50 | : 5

≠ = 2/5 + + 10


1: 2/5 + + 10 + + = 38 | - 10

7/5 + = 28 | ∋∋† 5/7


+ = 28 ∋∋† 5/7 = 4 ∋∋† 5

+ = 20


=&⊥†; ≠ + 20 = 38 | -20

≠ = 18

4≈†≠++†: 8;∞ ∂†∞;≈∞+∞ 5∋+† ;≈† 18, ⊇;∞ ⊥++ß∞+∞ 5∋+† ;≈† 20, ∋†≈+ +∞†+=⊥† ⊇;∞ 8;††∞+∞≈= 2.


+) ≠ = 4††∞+ ⊇∞≈ 2∋†∞+≈

+ = 4††∞+ ⊇∞≈ 1∞≈⊥∞≈


≠ – 1 = 3(+ – 1) = 3+ – 3 =&⊥†; ≠ – 3+ = - 2

≠ – 9 = 5(+ – 9) = 5+ – 45 =&⊥†; ≠ – 5+ = -36

--------

2+ = 34 =&⊥†; + = 17

≠ – 3∋∋† 17 = - 2 | +51

≠ = 49

4≈†≠++†: 4∂†∞∞†† ;≈† ⊇∞+ 2∋†∞+ 49 1∋++∞ ∞≈⊇ ⊇∞+ 3++≈ 17 1∋++∞ ∋††.


≤) ≠ = 1.5;††∞+, + = 2. 5;††∞+ = = 3.5;††∞+


= = 3 +

+ = ≠ – 5

≠ + + + = = 20


=&⊥†; ≠ + + + 3 + = 20

≠ + 4 + = 20

≠ + 4(≠ – 5) = 20

≠ + 4≠ – 20 = 20 | + 20

5 ≠ = 40 | : 5

≠ = 8

+ = 8 – 5

+ = 3

= = 3 ∋∋† 3

= = 9


4≈†≠++†: 8;∞ ⊥∞≈∞≤+†∞ .....



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