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2 cards from this section. Quick, good the night before a test.
What is the row space of a 2x3 matrix?
Think about what span means.
How do you determine if a vector is in the column space of a matrix?
Consider using row reduction.
What does the row space of a matrix represent?
Think about the definition of span.
True or False: The null space contains vectors that can be expressed as a linear combination of the row space.
Consider the definition of null space.
Given a matrix A with explicit entries, calculate the row space, column space, and null space. Provide a geometric interpretation.
Use row reduction and linear combination analyses.
Explain how changing one of the rows in matrix A affects the rank and nullity. Include an example with illustrations.
Visualize with a change in basis.
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