Unformatted text preview: 54 PROBLEMS FOR CHAPTER 1 For a system of three equations in three variables, the three equations represent three planes in
a three dimensional space. Geometrically, we have four cases. 1. The three plane intersects at one point, so the system has a unique solution. 2. The three planes do not have a point in common, so the system has no solution. (See Figure 2
for cases in which the three planes are distinct.) 3. The three plane intersects at a line, so there are inﬁnitely many solutions. 4. The three equations represent the same plane. Again, the system has inﬁnitely many solu—
tions. II if ik ...
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