1. Consider the linear system x+ y+ z = 2 r+ 2y + z = b -r+ 2y + az = 1 (a) For which values of a and b will the three planes intersect at a point? (b) For which values of a and b will the three planes intersect at a line? (c) For which values of a and b will the three planes intersect in a plane? (d) For which values of a and b will the three planes share no points of intersection?

1. Consider the linear system x+ y+ z = 2 r+ 2y + z = b -r+ 2y + az = 1 (a) For which values of a and b will the three planes intersect at a point? (b) For which values of a and b will the three planes intersect at a line? (c) For which values of a and b will the three planes intersect in a plane? (d) For which values of a and b will the three planes share no points of intersection?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter7: Conic Sections And Quadratic Systems

Section7.4: Solving Nonlinear Systems Of Equations

Problem 62E

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What is a system of linear equations in the variables x, y, and z?
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