22.4 - Methods to Find Rank
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Practice Questions
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What does the rank of a matrix indicate?
💡 Hint: Think about dimensions and independence.
Name one type of row operation.
💡 Hint: Consider operations that change row positions.
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Interactive Quizzes
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What is the rank of a zero matrix?
💡 Hint: Consider the definition of rank and its parameters.
To find the rank of a matrix, we count the number of non-zero rows in REF. Is this statement True or False?
💡 Hint: Think about how we define row echelon form.
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Challenge Problems
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Given the matrix \[ \begin{bmatrix} 1 & 2 & 3 \ 0 & 0 & 0 \ 4 & 5 & 6 \end{bmatrix} \], apply both methods to find its rank.
💡 Hint: Ensure to perform both calculations for confirmation.
Can you find the rank of the matrix \[ \begin{bmatrix} 1 & 2 \ 2 & 4 \ 3 & 6 \end{bmatrix}\]? What does this reveal about linear dependence?
💡 Hint: Remember to reduce the matrix carefully!
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