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

12 questions · Seed 104741 · 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 = [[5, 7], [3, 5]].
4
det(M) = (5 × 5) − (7 × 3) = 25 − 21 = 4.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [5, 9]].
59
det(M) = (11 × 9) − (8 × 5) = 99 − 40 = 59.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [6, 5]].
34
det(M) = (8 × 5) − (1 × 6) = 40 − 6 = 34.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [2, 5]].
2
det(M) = (2 × 5) − (4 × 2) = 10 − 8 = 2.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [7, 6]].
12
det(M) = (9 × 6) − (6 × 7) = 54 − 42 = 12.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [4, 4]].
36
det(M) = (11 × 4) − (2 × 4) = 44 − 8 = 36.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [9, 6]].
24
det(M) = (7 × 6) − (2 × 9) = 42 − 18 = 24.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [8, 4]].
4
det(M) = (9 × 4) − (4 × 8) = 36 − 32 = 4.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [4, 10]].
100
det(M) = (12 × 10) − (5 × 4) = 120 − 20 = 100.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 8]].
0
det(M) = (4 × 8) − (8 × 4) = 32 − 32 = 0.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [5, 11]].
82
det(M) = (12 × 11) − (10 × 5) = 132 − 50 = 82.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [4, 8]].
68
det(M) = (11 × 8) − (5 × 4) = 88 − 20 = 68.

12 questions · Seed 104741 · 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 = [[5, 7], [3, 5]].
M = [ 5 7 ; 3 5 ] · det(M) = (5×5) − (7×3)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [5, 9]].
M = [ 11 8 ; 5 9 ] · det(M) = (11×9) − (8×5)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [6, 5]].
M = [ 8 1 ; 6 5 ] · det(M) = (8×5) − (1×6)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [2, 5]].
M = [ 2 4 ; 2 5 ] · det(M) = (2×5) − (4×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [7, 6]].
M = [ 9 6 ; 7 6 ] · det(M) = (9×6) − (6×7)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [4, 4]].
M = [ 11 2 ; 4 4 ] · det(M) = (11×4) − (2×4)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [9, 6]].
M = [ 7 2 ; 9 6 ] · det(M) = (7×6) − (2×9)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [8, 4]].
M = [ 9 4 ; 8 4 ] · det(M) = (9×4) − (4×8)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [4, 10]].
M = [ 12 5 ; 4 10 ] · det(M) = (12×10) − (5×4)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 8]].
M = [ 4 8 ; 4 8 ] · det(M) = (4×8) − (8×4)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [5, 11]].
M = [ 12 10 ; 5 11 ] · det(M) = (12×11) − (10×5)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [4, 8]].
M = [ 11 5 ; 4 8 ] · det(M) = (11×8) − (5×4)

12 questions · Seed 104741 · 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 = [[5, 7], [3, 5]].
4
det(M) = (5 × 5) − (7 × 3) = 25 − 21 = 4.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [5, 9]].
59
det(M) = (11 × 9) − (8 × 5) = 99 − 40 = 59.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [6, 5]].
34
det(M) = (8 × 5) − (1 × 6) = 40 − 6 = 34.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [2, 5]].
2
det(M) = (2 × 5) − (4 × 2) = 10 − 8 = 2.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [7, 6]].
12
det(M) = (9 × 6) − (6 × 7) = 54 − 42 = 12.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [4, 4]].
36
det(M) = (11 × 4) − (2 × 4) = 44 − 8 = 36.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [9, 6]].
24
det(M) = (7 × 6) − (2 × 9) = 42 − 18 = 24.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [8, 4]].
4
det(M) = (9 × 4) − (4 × 8) = 36 − 32 = 4.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [4, 10]].
100
det(M) = (12 × 10) − (5 × 4) = 120 − 20 = 100.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 8]].
0
det(M) = (4 × 8) − (8 × 4) = 32 − 32 = 0.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [5, 11]].
82
det(M) = (12 × 11) − (10 × 5) = 132 − 50 = 82.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [4, 8]].
68
det(M) = (11 × 8) − (5 × 4) = 88 − 20 = 68.

12 questions · Seed 104741 · Age guidance, not curriculum certification