The graph of ax + by + cz = 0 is a plane through the origin (provided that not all of a, b, and c are zero). Use Theorem 1.3.1 to show that two planes through the origin have a point in common other than the origin (0, 0, 0). Theorem 1.3.1: If a homogeneous system of linear equations has more variables than equations, then it has a nontrivial solution (in fact, infinitely many).

The graph of ax + by + cz = 0 is a plane through the origin (provided that not all of a, b, and c are zero). Use Theorem 1.3.1 to show that two planes through the origin have a point in common other than the origin (0, 0, 0). Theorem 1.3.1: If a homogeneous system of linear equations has more variables than equations, then it has a nontrivial solution (in fact, infinitely many).

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.5: Cramer's Rule

Problem 35PS

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