Practice Method 2: Using Minors (22.4.2) - Rank of a Matrix

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6 sample questions

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

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