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4 cards from this section. Quick, good the night before a test.
What does an intersection of two lines represent in R2?
Think about how many solutions can exist.
What is indicated if two planes in R3 are parallel?
Recall the relationship between parallel lines and solutions.
What does it mean if two lines in R2 do not intersect?
Think about how lines can relate to one another.
In three dimensions, if two planes intersect, what is the possible solution type?
Visualize the intersection carefully.
Given the equations y = 2x + 3, y = -1x + 1, and z = x + 2y - 4, analyze the solution set geometrically.
Visualize how these intersect on paper.
Construct a scenario using three planes in R3 that are parallel and do not share any solutions. Describe the implications.
Consider how adding a constant to a plane keeps them parallel.
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