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4 cards from this section. Quick, good the night before a test.
Define rank in the context of a matrix.
Think about the dimensions of the space these dimensions span.
What does nullity measure?
Consider what happens when the equation has free variables.
What does the Rank-Nullity Theorem state?
Think about the dimensions involved in the matrix.
If a matrix has a rank of 0, what can you say about its nullity?
Reflect on how free variables correlate with rank.
A matrix has 6 columns and a rank of 2. Determine its nullity and discuss what it implies about the solution to the equation Ax=0.
Use the Rank-Nullity theorem to find nullity.
Consider a system represented by a matrix with rank m. If the system has n variables, derive the implications for the existence of solutions based on the values of m and n.
Reflect on the implications of rank relative to the number of variables.
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