Practice question · Sort into groups
Sort each fact by what it does to a determinant.
Groups: Makes it zero · Changes its sign · Leaves it unchanged
- Two identical rows
- Transposing the matrix
- One column is 5× another column
- A full row of zeros
- Swapping two rows
Hints
- Ask whether the operation introduces redundancy, flips orientation, or changes nothing.
- Swapping two rows affects the sign but not the magnitude.
Show the answer
Makes it zero: A full row of zeros, Two identical rows, One column is 5× another column
Changes its sign: Swapping two rows
Leaves it unchanged: Transposing the matrix
Why
Redundancy (zeros, copies, proportionality) kills the determinant; a swap flips orientation; transposition changes nothing, rows and columns tell the same story.
Practise Determinants
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