 By Kleshchev A.S.

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Dieses Buch mit seinen zahlreichen Fragen und Antworten sowie Aufgaben und Lösungen wendet sich vorwiegend an Studierende natur- und ingenieurwissenschaftlicher Studiengänge der ersten Semester an Technischen Universitäten und Fachhochschulen. Im Mittelpunkt stehen Vektoren, Determinanten und Matrizen, lineare Gleichungssysteme, Eigenwerte und Eigenvektoren quadratischer Matrizen, Gerade und Ebene im Raum, Verschiebung und Drehung von Koordinatensystemen, Kegelschnitte.

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How many pounds of each should I buy? b. If I suddenly realize I need to set aside \$5 to buy chips, can I still buy 5 pounds of nuts with the remaining \$10? c. s the greatest amount of nuts I can buy? 14. A chemistry experiment calls for one liter of sulfuric acid at a 15% concentration, but the supply room only stocks sulfuric acid in concentrations of 10% and 35%. a. How many liters of each should be mixed to give the acid needed for the experiment? b. How many liters should be mixed to give two liters at a 15% concentration?

A. b. (-4, 3) c. 5. a. (4, -2) b. (1, -8) c. (-2, 5) Solve the following systems using the graphing method. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Try to solve the following system using the graphing method: . a. What does it look like the coordinate of the solution should be? b. Does that coordinate really give the same value when you plug it into both equations? c. Why is it difficult to find the real solution to this system? 17. Try to solve the following system using the graphing method: .

For example, what happens if we swap the directions of the inequality signs in the system we just graphed? To graph the system , we draw the same lines we drew for the previous system, but we shade upward for the first inequality and downward for the second inequality. Here is the result: You can see that this time the shaded regions overlap. The area between the two lines is the solution to the system. one that continues infinitely in at least one direction. a finite region with three or more sides.