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

12 questions · Seed 57 · 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 = [[10, 3], [7, 11]].
89
det(M) = (10 × 11) − (3 × 7) = 110 − 21 = 89.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [7, 9]].
-16
det(M) = (6 × 9) − (10 × 7) = 54 − 70 = -16.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 10], [5, 5]].
-35
det(M) = (3 × 5) − (10 × 5) = 15 − 50 = -35.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [6, 4]].
-8
det(M) = (7 × 4) − (6 × 6) = 28 − 36 = -8.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [7, 9]].
29
det(M) = (11 × 9) − (10 × 7) = 99 − 70 = 29.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 9], [8, 9]].
18
det(M) = (10 × 9) − (9 × 8) = 90 − 72 = 18.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 3], [3, 4]].
39
det(M) = (12 × 4) − (3 × 3) = 48 − 9 = 39.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [8, 3]].
11
det(M) = (9 × 3) − (2 × 8) = 27 − 16 = 11.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [5, 4]].
-9
det(M) = (4 × 4) − (5 × 5) = 16 − 25 = -9.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [6, 8]].
-14
det(M) = (5 × 8) − (9 × 6) = 40 − 54 = -14.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [4, 4]].
4
det(M) = (3 × 4) − (2 × 4) = 12 − 8 = 4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [10, 11]].
38
det(M) = (8 × 11) − (5 × 10) = 88 − 50 = 38.

12 questions · Seed 57 · 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 = [[10, 3], [7, 11]].
M = [ 10 3 ; 7 11 ] · det(M) = (10×11) − (3×7)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [7, 9]].
M = [ 6 10 ; 7 9 ] · det(M) = (6×9) − (10×7)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 10], [5, 5]].
M = [ 3 10 ; 5 5 ] · det(M) = (3×5) − (10×5)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [6, 4]].
M = [ 7 6 ; 6 4 ] · det(M) = (7×4) − (6×6)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [7, 9]].
M = [ 11 10 ; 7 9 ] · det(M) = (11×9) − (10×7)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 9], [8, 9]].
M = [ 10 9 ; 8 9 ] · det(M) = (10×9) − (9×8)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 3], [3, 4]].
M = [ 12 3 ; 3 4 ] · det(M) = (12×4) − (3×3)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [8, 3]].
M = [ 9 2 ; 8 3 ] · det(M) = (9×3) − (2×8)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [5, 4]].
M = [ 4 5 ; 5 4 ] · det(M) = (4×4) − (5×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [6, 8]].
M = [ 5 9 ; 6 8 ] · det(M) = (5×8) − (9×6)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [4, 4]].
M = [ 3 2 ; 4 4 ] · det(M) = (3×4) − (2×4)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [10, 11]].
M = [ 8 5 ; 10 11 ] · det(M) = (8×11) − (5×10)

12 questions · Seed 57 · 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 = [[10, 3], [7, 11]].
89
det(M) = (10 × 11) − (3 × 7) = 110 − 21 = 89.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [7, 9]].
-16
det(M) = (6 × 9) − (10 × 7) = 54 − 70 = -16.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 10], [5, 5]].
-35
det(M) = (3 × 5) − (10 × 5) = 15 − 50 = -35.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [6, 4]].
-8
det(M) = (7 × 4) − (6 × 6) = 28 − 36 = -8.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [7, 9]].
29
det(M) = (11 × 9) − (10 × 7) = 99 − 70 = 29.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 9], [8, 9]].
18
det(M) = (10 × 9) − (9 × 8) = 90 − 72 = 18.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 3], [3, 4]].
39
det(M) = (12 × 4) − (3 × 3) = 48 − 9 = 39.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [8, 3]].
11
det(M) = (9 × 3) − (2 × 8) = 27 − 16 = 11.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [5, 4]].
-9
det(M) = (4 × 4) − (5 × 5) = 16 − 25 = -9.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [6, 8]].
-14
det(M) = (5 × 8) − (9 × 6) = 40 − 54 = -14.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [4, 4]].
4
det(M) = (3 × 4) − (2 × 4) = 12 − 8 = 4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [10, 11]].
38
det(M) = (8 × 11) − (5 × 10) = 88 − 50 = 38.

12 questions · Seed 57 · Age guidance, not curriculum certification