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The document provides solutions for mathematical problems from Lambacher Schweizer Qualifikationsphase NRW, focusing on linear equations and vector geometry.
Key points:
• Detailed solutions for exercises 4, 7, and 10 from page 238
• Includes vector equations, parametric forms, and linear systems
• Demonstrates use of graphing calculator (GTR) for solving linear systems
• Covers topics relevant for Lambacher Schweizer Qualifikationsphase Leistungskurs
26.4.2021
1690
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FGeGfOWaMcjdsEjfxjkak_image_page_1.webp&w=828&q=75)
This page continues with solutions for exercise 7d and introduces new geometric problems involving points and vectors in three-dimensional space. The solutions demonstrate more complex applications of vector equations and parametric forms.
Example: For Figure 1, the solution provides the vector equation: E = 3 + t(-6, -4, -1) + s(10, 4, 10)
The page includes solutions for two geometric figures, each involving three points in space. These problems require students to determine vector equations of lines and planes passing through given points.
Highlight: The solutions on this page are particularly relevant for students using the Lambacher Schweizer Qualifikationsphase Arbeitsheft, as they provide detailed workings for complex geometric problems.
Definition: Parametric form - A way of representing a geometric object (like a line or plane) using parameters, allowing for a more flexible description of its position in space.
The page concludes with a system of linear equations representing a plane: 15x + 6y + 10z = 30 6x + 1.5y - 42 = 6
These problems showcase the integration of vector geometry and linear algebra, which is a key focus in the Lambacher Schweizer Qualifikationsphase PDF materials.
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FjgWkZJyQCfRWoYlcIcds_image_page_1.webp&w=828&q=75)
This page presents solutions for exercises 4 and 7 from page 238 of the Lambacher Schweizer Qualifikationsphase textbook. The problems involve solving systems of linear equations and working with vector equations.
Example: For problem 4a, the solution shows the vector equation: E = 2 + r(-7, 12, 5) + s(0, 1, 2)
The page demonstrates the use of parametric forms to represent lines and planes in three-dimensional space. It also includes solutions for linear systems using the graphing calculator's linsolve function.
Highlight: The solutions make extensive use of vector notation and parametric equations, which are key concepts in the Lambacher Schweizer Qualifikationsphase Leistungskurs.
Vocabulary: GTR linsolve - A function on graphing calculators used to solve systems of linear equations.
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FGeGfOWaMcjdsEjfxjkak_image_page_2.webp&w=828&q=75)
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FjgWkZJyQCfRWoYlcIcds_image_page_2.webp&w=828&q=75)
116
3469
11
Polynomdivision Präsi
Polynomdivision/ Substitution/ Resubstitution
2
108
11/12
Dreieckssystem-lineares Gleichungssystem
Hier habe ich 2 Rechnungen vom Lösen eines linearen Gleichungssystems mit dem Dreieckssystem erstellt
59
2237
11/12
Lambacher Schweizer Qualifikationsphase GK LK
S. 244, 3, 5, 1a S. 245, 6, 7, 10
8
75
11/12
Kurvendiskussion
Dieses Know beinhaltet alle Schritte, die in einer Kurvendiskussion benötigt werden sowie die Bestimmung von Funktionsgleichungen anhand von Steckbriefaufgaben. Zudem behandelt dieses Know noch den Gauß-Algorithmus🥰
295
9053
Lineares Gleichungssystem
Lineares Gleichungssystem, Vektoren, Orientierung im Raum, linearkombination, komplanare Vektoren,
29
1908
11
Gaußverfahren
Erklärung des Gaußverfahren
Durchschnittliche App-Bewertung
Schüler:innen lieben Knowunity
In Bildungs-App-Charts in 12 Ländern
Schüler:innen haben Lernzettel hochgeladen
iOS User
Philipp, iOS User
Lena, iOS Userin
The document provides solutions for mathematical problems from Lambacher Schweizer Qualifikationsphase NRW, focusing on linear equations and vector geometry.
Key points:
• Detailed solutions for exercises 4, 7, and 10 from page 238
• Includes vector equations, parametric forms, and linear systems
• Demonstrates use of graphing calculator (GTR) for solving linear systems
• Covers topics relevant for Lambacher Schweizer Qualifikationsphase Leistungskurs
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FGeGfOWaMcjdsEjfxjkak_image_page_1.webp&w=2048&q=75)
This page continues with solutions for exercise 7d and introduces new geometric problems involving points and vectors in three-dimensional space. The solutions demonstrate more complex applications of vector equations and parametric forms.
Example: For Figure 1, the solution provides the vector equation: E = 3 + t(-6, -4, -1) + s(10, 4, 10)
The page includes solutions for two geometric figures, each involving three points in space. These problems require students to determine vector equations of lines and planes passing through given points.
Highlight: The solutions on this page are particularly relevant for students using the Lambacher Schweizer Qualifikationsphase Arbeitsheft, as they provide detailed workings for complex geometric problems.
Definition: Parametric form - A way of representing a geometric object (like a line or plane) using parameters, allowing for a more flexible description of its position in space.
The page concludes with a system of linear equations representing a plane: 15x + 6y + 10z = 30 6x + 1.5y - 42 = 6
These problems showcase the integration of vector geometry and linear algebra, which is a key focus in the Lambacher Schweizer Qualifikationsphase PDF materials.
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FjgWkZJyQCfRWoYlcIcds_image_page_1.webp&w=2048&q=75)
This page presents solutions for exercises 4 and 7 from page 238 of the Lambacher Schweizer Qualifikationsphase textbook. The problems involve solving systems of linear equations and working with vector equations.
Example: For problem 4a, the solution shows the vector equation: E = 2 + r(-7, 12, 5) + s(0, 1, 2)
The page demonstrates the use of parametric forms to represent lines and planes in three-dimensional space. It also includes solutions for linear systems using the graphing calculator's linsolve function.
Highlight: The solutions make extensive use of vector notation and parametric equations, which are key concepts in the Lambacher Schweizer Qualifikationsphase Leistungskurs.
Vocabulary: GTR linsolve - A function on graphing calculators used to solve systems of linear equations.
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FGeGfOWaMcjdsEjfxjkak_image_page_2.webp&w=2048&q=75)
![Seite 238, nr. 4 & 7 c, d, 10
4a)
7c)
2
E*-(1)-¹ (1) ₁ (3)
= +r.
+ S.
10₁ + 3n₂ = 0
-2n₁ +10₂ +3n3-0
g
n = -3
€ [1-(4)] (9)-0
E:
9x-3y +72 =](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FjgWkZJyQCfRWoYlcIcds_image_page_2.webp&w=2048&q=75)
Mathe - Polynomdivision Präsi
Polynomdivision/ Substitution/ Resubstitution
116
3469
1
Mathe - Dreieckssystem-lineares Gleichungssystem
Hier habe ich 2 Rechnungen vom Lösen eines linearen Gleichungssystems mit dem Dreieckssystem erstellt
2
108
0
Mathe - Lambacher Schweizer Qualifikationsphase GK LK
S. 244, 3, 5, 1a S. 245, 6, 7, 10
59
2237
0
Mathe - Kurvendiskussion
Dieses Know beinhaltet alle Schritte, die in einer Kurvendiskussion benötigt werden sowie die Bestimmung von Funktionsgleichungen anhand von Steckbriefaufgaben. Zudem behandelt dieses Know noch den Gauß-Algorithmus🥰
8
75
0
Mathe - Lineares Gleichungssystem
Lineares Gleichungssystem, Vektoren, Orientierung im Raum, linearkombination, komplanare Vektoren,
295
9053
12
Mathe - Gaußverfahren
Erklärung des Gaußverfahren
29
1908
0
Durchschnittliche App-Bewertung
Schüler:innen lieben Knowunity
In Bildungs-App-Charts in 12 Ländern
Schüler:innen haben Lernzettel hochgeladen
iOS User
Philipp, iOS User
Lena, iOS Userin
