In Exercises 16-18, determine whether the given (2 x 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, give equa- tions of the form x = at+b, y = ct+d, z = et + f. 16. 2x₁ + x2 + x3 = 3 -2x₁ + x₂-x3 = 1 18. x₁ + 3x2 - 2xy = -1 2x₁ + 6x - 4x = -2 17. x₁ + 2x₂-x3 = 2 x₁ + x₂ + x3 = 3
In Exercises 16-18, determine whether the given (2 x 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, give equa- tions of the form x = at+b, y = ct+d, z = et + f. 16. 2x₁ + x2 + x3 = 3 -2x₁ + x₂-x3 = 1 18. x₁ + 3x2 - 2xy = -1 2x₁ + 6x - 4x = -2 17. x₁ + 2x₂-x3 = 2 x₁ + x₂ + x3 = 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can I get the answers for 16 and 18
Transcribed Image Text:In Exercises 16-18, determine whether the given (2 x 3)
system of linear equations represents coincident planes
(that is, the same plane), two parallel planes, or two
planes whose intersection is a line. In the latter case, give
the parametric equations for the line; that is, give equa-
tions of the form x = at +b, y = ct+d, z = et + f.
16. 2x₁ + x₂ + x3 = 3 17. x₁ + 2x₂x3 = 2
-2x₁ + x₂x3 = 1 x₁ + x₂ + x3 = 3
18. x₁ + 3x₂ - 2x3 = -1
2x₁ + 6x2 - 4x3 = -2
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