Practice question · Sort into groups
Sort each 2x2 matrix by whether it is invertible (nonzero determinant).
Groups: Invertible · Singular
- rows (2, 6) and (1, 3)
- rows (5, 0) and (0, 2)
- rows (4, 4) and (1, 1)
- rows (1, 2) and (3, 4)
Hints
- Compute ad - bc; zero means singular.
- m2 and m4 each have one row a multiple of the other.
Show the answer
Invertible: rows (1, 2) and (3, 4), rows (5, 0) and (0, 2)
Singular: rows (2, 6) and (1, 3), rows (4, 4) and (1, 1)
Why
m1: 1*4 - 2*3 = -2 (nonzero, invertible). m3: 5*2 - 0 = 10 (invertible). m2: 2*3 - 6*1 = 0 and m4: 4*1 - 4*1 = 0 are both singular, their rows are proportional.
Practise Determinants and Invertibility
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