Practice question · Select all that apply
Select every matrix below whose determinant is 0.
Hints
- Compute ad - bc for each, or look for a zero row or proportional rows.
- The determinants are 0, 8, 0, 0 and -1.
Show the answer
- A. rows (0, 0) and (5, 7)
- D. rows (1, 2) and (2, 4)
- E. rows (2, 3) and (4, 6)
Why
Options 1 and 4 have proportional rows and option 1 has a zero row, all forcing determinant 0. Option 2 gives 9 - 1 = 8 and option 2 gives -1, nonzero, hence invertible. A negative determinant is not a zero determinant, which is the trap in the second option.
Practise Determinants
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