MathsAges 16-18

2×2 matrix determinants

Evaluate the determinant det(M) = ad − bc of a 2 × 2 matrix from its leading and secondary diagonals. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

2×2 matrix determinants

Take your time. Show your thinking.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [3, 8]].
M = [ 2 9 ; 3 8 ] · det(M) = (2×8) − (9×3)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [6, 3]].
M = [ 3 5 ; 6 3 ] · det(M) = (3×3) − (5×6)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [8, 9]].
M = [ 12 2 ; 8 9 ] · det(M) = (12×9) − (2×8)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [3, 6]].
M = [ 10 5 ; 3 6 ] · det(M) = (10×6) − (5×3)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [1, 7]].
M = [ 12 5 ; 1 7 ] · det(M) = (12×7) − (5×1)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [4, 2]].
M = [ 6 1 ; 4 2 ] · det(M) = (6×2) − (1×4)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [2, 3]].
M = [ 10 2 ; 2 3 ] · det(M) = (10×3) − (2×2)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [6, 4]].
M = [ 2 6 ; 6 4 ] · det(M) = (2×4) − (6×6)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [3, 6]].
M = [ 11 8 ; 3 6 ] · det(M) = (11×6) − (8×3)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [7, 5]].
M = [ 4 9 ; 7 5 ] · det(M) = (4×5) − (9×7)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 6], [1, 5]].
M = [ 6 6 ; 1 5 ] · det(M) = (6×5) − (6×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 6], [2, 11]].
M = [ 5 6 ; 2 11 ] · det(M) = (5×11) − (6×2)

12 questions · Seed 47 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

2×2 matrix determinants

Answers and reasoning. Review before teaching.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [3, 8]].
-11
det(M) = (2 × 8) − (9 × 3) = 16 − 27 = -11.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [6, 3]].
-21
det(M) = (3 × 3) − (5 × 6) = 9 − 30 = -21.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [8, 9]].
92
det(M) = (12 × 9) − (2 × 8) = 108 − 16 = 92.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [3, 6]].
45
det(M) = (10 × 6) − (5 × 3) = 60 − 15 = 45.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [1, 7]].
79
det(M) = (12 × 7) − (5 × 1) = 84 − 5 = 79.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [4, 2]].
8
det(M) = (6 × 2) − (1 × 4) = 12 − 4 = 8.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [2, 3]].
26
det(M) = (10 × 3) − (2 × 2) = 30 − 4 = 26.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [6, 4]].
-28
det(M) = (2 × 4) − (6 × 6) = 8 − 36 = -28.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [3, 6]].
42
det(M) = (11 × 6) − (8 × 3) = 66 − 24 = 42.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [7, 5]].
-43
det(M) = (4 × 5) − (9 × 7) = 20 − 63 = -43.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 6], [1, 5]].
24
det(M) = (6 × 5) − (6 × 1) = 30 − 6 = 24.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 6], [2, 11]].
43
det(M) = (5 × 11) − (6 × 2) = 55 − 12 = 43.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

2×2 matrix determinants

Take your time. Show your thinking.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [3, 8]].
M = [ 2 9 ; 3 8 ] · det(M) = (2×8) − (9×3)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [6, 3]].
M = [ 3 5 ; 6 3 ] · det(M) = (3×3) − (5×6)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [8, 9]].
M = [ 12 2 ; 8 9 ] · det(M) = (12×9) − (2×8)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [3, 6]].
M = [ 10 5 ; 3 6 ] · det(M) = (10×6) − (5×3)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [1, 7]].
M = [ 12 5 ; 1 7 ] · det(M) = (12×7) − (5×1)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [4, 2]].
M = [ 6 1 ; 4 2 ] · det(M) = (6×2) − (1×4)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [2, 3]].
M = [ 10 2 ; 2 3 ] · det(M) = (10×3) − (2×2)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [6, 4]].
M = [ 2 6 ; 6 4 ] · det(M) = (2×4) − (6×6)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [3, 6]].
M = [ 11 8 ; 3 6 ] · det(M) = (11×6) − (8×3)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [7, 5]].
M = [ 4 9 ; 7 5 ] · det(M) = (4×5) − (9×7)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 6], [1, 5]].
M = [ 6 6 ; 1 5 ] · det(M) = (6×5) − (6×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 6], [2, 11]].
M = [ 5 6 ; 2 11 ] · det(M) = (5×11) − (6×2)

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

2×2 matrix determinants

Answers and reasoning. Review before teaching.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [3, 8]].
-11
det(M) = (2 × 8) − (9 × 3) = 16 − 27 = -11.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [6, 3]].
-21
det(M) = (3 × 3) − (5 × 6) = 9 − 30 = -21.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [8, 9]].
92
det(M) = (12 × 9) − (2 × 8) = 108 − 16 = 92.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [3, 6]].
45
det(M) = (10 × 6) − (5 × 3) = 60 − 15 = 45.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [1, 7]].
79
det(M) = (12 × 7) − (5 × 1) = 84 − 5 = 79.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [4, 2]].
8
det(M) = (6 × 2) − (1 × 4) = 12 − 4 = 8.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [2, 3]].
26
det(M) = (10 × 3) − (2 × 2) = 30 − 4 = 26.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [6, 4]].
-28
det(M) = (2 × 4) − (6 × 6) = 8 − 36 = -28.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [3, 6]].
42
det(M) = (11 × 6) − (8 × 3) = 66 − 24 = 42.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [7, 5]].
-43
det(M) = (4 × 5) − (9 × 7) = 20 − 63 = -43.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 6], [1, 5]].
24
det(M) = (6 × 5) − (6 × 1) = 30 − 6 = 24.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 6], [2, 11]].
43
det(M) = (5 × 11) − (6 × 2) = 55 − 12 = 43.

12 questions · Seed 47 · Age guidance, not curriculum certification