21.5.2 - Methods to Find Rank
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Practice Questions
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Define the rank of a matrix.
💡 Hint: Think about linear independence.
What is echelon form?
💡 Hint: Visualize a staircase.
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Interactive Quizzes
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What is the definition of rank?
💡 Hint: Focus on linear independence.
True or False: Rank can only be determined using echelon form.
💡 Hint: Think about different methods available to find rank.
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Challenge Problems
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Given the \(4 \times 4\) matrix \(C = \begin{bmatrix} 1 & 0 & 0 & 5 \ 0 & 0 & 0 & 0 \ 0 & 2 & 1 & 3 \ 0 & 0 & 0 & 0 \end{bmatrix}\), find the rank after performing row reduction.
💡 Hint: Focus on reducing the matrix to echelon form first.
A \(2 \times 3\) matrix \(D\) has a rank of 2. If you added a third row that is a linear combination of the existing rows, what would the new rank be?
💡 Hint: Consider the implications of linear combinations on independence.
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