22.4.2 - Method 2: Using Minors
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Practice Questions
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What is the rank of a matrix if all rows are linearly independent?
💡 Hint: Think about linear independence!
Define a minor in the context of matrices.
💡 Hint: Consider the relationship with determinants.
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Interactive Quizzes
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What method are we using to determine the rank of the matrix?
💡 Hint: Think about the method that involves determinants!
True or False: The rank of a matrix can be determined solely by the size of the matrix.
💡 Hint: Consider what affects linear independence!
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Challenge Problems
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Consider the matrix \( C = \begin{bmatrix} 1 & 2 & 3 \ 0 & 0 & 0 \ 2 & 4 & 6 \end{bmatrix} \). Determine its rank using minors.
💡 Hint: Reflect on linear dependencies!
For the matrix \( D = \begin{bmatrix} 2 & 3 & 5 \ 1 & 0 & 4 \ 3 & 6 & 7 \end{bmatrix} \), compute the rank and explain.
💡 Hint: Examine the submatrices carefully for dependencies.
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