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

12 questions · Seed 104734 · 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 = [[8, 3], [9, 10]].
53
det(M) = (8 × 10) − (3 × 9) = 80 − 27 = 53.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 10]].
68
det(M) = (10 × 10) − (8 × 4) = 100 − 32 = 68.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 11]].
78
det(M) = (10 × 11) − (8 × 4) = 110 − 32 = 78.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [2, 12]].
76
det(M) = (8 × 12) − (10 × 2) = 96 − 20 = 76.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [10, 3]].
-13
det(M) = (9 × 3) − (4 × 10) = 27 − 40 = -13.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [2, 3]].
7
det(M) = (7 × 3) − (7 × 2) = 21 − 14 = 7.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [1, 7]].
74
det(M) = (11 × 7) − (3 × 1) = 77 − 3 = 74.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [4, 3]].
-17
det(M) = (5 × 3) − (8 × 4) = 15 − 32 = -17.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [4, 10]].
34
det(M) = (7 × 10) − (9 × 4) = 70 − 36 = 34.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 8]].
48
det(M) = (10 × 8) − (8 × 4) = 80 − 32 = 48.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [6, 5]].
-21
det(M) = (3 × 5) − (6 × 6) = 15 − 36 = -21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [3, 7]].
61
det(M) = (10 × 7) − (3 × 3) = 70 − 9 = 61.

12 questions · Seed 104734 · 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 = [[8, 3], [9, 10]].
M = [ 8 3 ; 9 10 ] · det(M) = (8×10) − (3×9)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 10]].
M = [ 10 8 ; 4 10 ] · det(M) = (10×10) − (8×4)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 11]].
M = [ 10 8 ; 4 11 ] · det(M) = (10×11) − (8×4)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [2, 12]].
M = [ 8 10 ; 2 12 ] · det(M) = (8×12) − (10×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [10, 3]].
M = [ 9 4 ; 10 3 ] · det(M) = (9×3) − (4×10)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [2, 3]].
M = [ 7 7 ; 2 3 ] · det(M) = (7×3) − (7×2)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [1, 7]].
M = [ 11 3 ; 1 7 ] · det(M) = (11×7) − (3×1)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [4, 3]].
M = [ 5 8 ; 4 3 ] · det(M) = (5×3) − (8×4)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [4, 10]].
M = [ 7 9 ; 4 10 ] · det(M) = (7×10) − (9×4)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 8]].
M = [ 10 8 ; 4 8 ] · det(M) = (10×8) − (8×4)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [6, 5]].
M = [ 3 6 ; 6 5 ] · det(M) = (3×5) − (6×6)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [3, 7]].
M = [ 10 3 ; 3 7 ] · det(M) = (10×7) − (3×3)

12 questions · Seed 104734 · 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 = [[8, 3], [9, 10]].
53
det(M) = (8 × 10) − (3 × 9) = 80 − 27 = 53.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 10]].
68
det(M) = (10 × 10) − (8 × 4) = 100 − 32 = 68.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 11]].
78
det(M) = (10 × 11) − (8 × 4) = 110 − 32 = 78.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [2, 12]].
76
det(M) = (8 × 12) − (10 × 2) = 96 − 20 = 76.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [10, 3]].
-13
det(M) = (9 × 3) − (4 × 10) = 27 − 40 = -13.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [2, 3]].
7
det(M) = (7 × 3) − (7 × 2) = 21 − 14 = 7.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [1, 7]].
74
det(M) = (11 × 7) − (3 × 1) = 77 − 3 = 74.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [4, 3]].
-17
det(M) = (5 × 3) − (8 × 4) = 15 − 32 = -17.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [4, 10]].
34
det(M) = (7 × 10) − (9 × 4) = 70 − 36 = 34.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [4, 8]].
48
det(M) = (10 × 8) − (8 × 4) = 80 − 32 = 48.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [6, 5]].
-21
det(M) = (3 × 5) − (6 × 6) = 15 − 36 = -21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [3, 7]].
61
det(M) = (10 × 7) − (3 × 3) = 70 − 9 = 61.

12 questions · Seed 104734 · Age guidance, not curriculum certification