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

12 questions · Seed 59 · 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 = [[3, 7], [10, 12]].
-34
det(M) = (3 × 12) − (7 × 10) = 36 − 70 = -34.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [9, 6]].
33
det(M) = (10 × 6) − (3 × 9) = 60 − 27 = 33.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [8, 12]].
80
det(M) = (10 × 12) − (5 × 8) = 120 − 40 = 80.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [9, 12]].
3
det(M) = (7 × 12) − (9 × 9) = 84 − 81 = 3.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [10, 12]].
50
det(M) = (10 × 12) − (7 × 10) = 120 − 70 = 50.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [7, 11]].
18
det(M) = (8 × 11) − (10 × 7) = 88 − 70 = 18.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [10, 8]].
24
det(M) = (8 × 8) − (4 × 10) = 64 − 40 = 24.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [2, 6]].
4
det(M) = (4 × 6) − (10 × 2) = 24 − 20 = 4.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [7, 4]].
-35
det(M) = (7 × 4) − (9 × 7) = 28 − 63 = -35.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [7, 3]].
-9
det(M) = (4 × 3) − (3 × 7) = 12 − 21 = -9.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [10, 5]].
5
det(M) = (11 × 5) − (5 × 10) = 55 − 50 = 5.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 6], [3, 6]].
12
det(M) = (5 × 6) − (6 × 3) = 30 − 18 = 12.

12 questions · Seed 59 · 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 = [[3, 7], [10, 12]].
M = [ 3 7 ; 10 12 ] · det(M) = (3×12) − (7×10)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [9, 6]].
M = [ 10 3 ; 9 6 ] · det(M) = (10×6) − (3×9)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [8, 12]].
M = [ 10 5 ; 8 12 ] · det(M) = (10×12) − (5×8)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [9, 12]].
M = [ 7 9 ; 9 12 ] · det(M) = (7×12) − (9×9)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [10, 12]].
M = [ 10 7 ; 10 12 ] · det(M) = (10×12) − (7×10)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [7, 11]].
M = [ 8 10 ; 7 11 ] · det(M) = (8×11) − (10×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [10, 8]].
M = [ 8 4 ; 10 8 ] · det(M) = (8×8) − (4×10)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [2, 6]].
M = [ 4 10 ; 2 6 ] · det(M) = (4×6) − (10×2)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [7, 4]].
M = [ 7 9 ; 7 4 ] · det(M) = (7×4) − (9×7)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [7, 3]].
M = [ 4 3 ; 7 3 ] · det(M) = (4×3) − (3×7)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [10, 5]].
M = [ 11 5 ; 10 5 ] · det(M) = (11×5) − (5×10)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 6], [3, 6]].
M = [ 5 6 ; 3 6 ] · det(M) = (5×6) − (6×3)

12 questions · Seed 59 · 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 = [[3, 7], [10, 12]].
-34
det(M) = (3 × 12) − (7 × 10) = 36 − 70 = -34.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [9, 6]].
33
det(M) = (10 × 6) − (3 × 9) = 60 − 27 = 33.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [8, 12]].
80
det(M) = (10 × 12) − (5 × 8) = 120 − 40 = 80.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [9, 12]].
3
det(M) = (7 × 12) − (9 × 9) = 84 − 81 = 3.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [10, 12]].
50
det(M) = (10 × 12) − (7 × 10) = 120 − 70 = 50.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [7, 11]].
18
det(M) = (8 × 11) − (10 × 7) = 88 − 70 = 18.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [10, 8]].
24
det(M) = (8 × 8) − (4 × 10) = 64 − 40 = 24.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [2, 6]].
4
det(M) = (4 × 6) − (10 × 2) = 24 − 20 = 4.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [7, 4]].
-35
det(M) = (7 × 4) − (9 × 7) = 28 − 63 = -35.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [7, 3]].
-9
det(M) = (4 × 3) − (3 × 7) = 12 − 21 = -9.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [10, 5]].
5
det(M) = (11 × 5) − (5 × 10) = 55 − 50 = 5.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 6], [3, 6]].
12
det(M) = (5 × 6) − (6 × 3) = 30 − 18 = 12.

12 questions · Seed 59 · Age guidance, not curriculum certification