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For any number k E R there is given a system of linear equations: х — 2у —z%3 1 x +z=-1 -х — у +z%3-1 x - y – 3 z=k (a) Determine for any value of k the complete solution to system. In the following questions, consider four planes in a standard (x, y, z)- coordinate system describes by the four equations stated above. (b) For k=9 the four planes outline a tetrahedron. Determine the area of the side face in tetrahedron which is equal to the fourth equation in the system of linear equations states above. (c) Determine the volume of the tetrahedron mentioned in (b). Is there any other values for k for which the four planes outline a tetrahedron of same volume?

For any number k E R there is given a system of linear equations: х — 2у —z%3 1 x +z=-1 -х — у +z%3-1 x - y – 3 z=k (a) Determine for any value of k the complete solution to system. In the following questions, consider four planes in a standard (x, y, z)- coordinate system describes by the four equations stated above. (b) For k=9 the four planes outline a tetrahedron. Determine the area of the side face in tetrahedron which is equal to the fourth equation in the system of linear equations states above. (c) Determine the volume of the tetrahedron mentioned in (b). Is there any other values for k for which the four planes outline a tetrahedron of same volume?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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For any number k E R there is given a system of linear equations: х — 2у —z%3 1 x +z=-1 -х — у +z%3-1 x - y – 3 z=k (a) Determine for any value of k the complete solution to system. In the following questions, consider four planes in a standard (x, y, z)- coordinate system describes by the four equations stated above. (b) For k=9 the four planes outline a tetrahedron. Determine the area of the side face in tetrahedron which is equal to the fourth equation in the system of linear equations states above. (c) Determine the volume of the tetrahedron mentioned in (b). Is there any other values for k for which the four planes outline a tetrahedron of same volume?
Transcribed Image Text:For any number k E R there is given a system of linear equations: х — 2у —z%3 1 x +z=-1 -х — у +z%3-1 x - y – 3 z=k (a) Determine for any value of k the complete solution to system. In the following questions, consider four planes in a standard (x, y, z)- coordinate system describes by the four equations stated above. (b) For k=9 the four planes outline a tetrahedron. Determine the area of the side face in tetrahedron which is equal to the fourth equation in the system of linear equations states above. (c) Determine the volume of the tetrahedron mentioned in (b). Is there any other values for k for which the four planes outline a tetrahedron of same volume?
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