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

12 questions · Seed 104743 · 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 = [[9, 7], [1, 2]].
11
det(M) = (9 × 2) − (7 × 1) = 18 − 7 = 11.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [2, 4]].
-6
det(M) = (2 × 4) − (7 × 2) = 8 − 14 = -6.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [2, 7]].
66
det(M) = (10 × 7) − (2 × 2) = 70 − 4 = 66.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [10, 12]].
10
det(M) = (5 × 12) − (5 × 10) = 60 − 50 = 10.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [4, 2]].
-6
det(M) = (11 × 2) − (7 × 4) = 22 − 28 = -6.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [7, 5]].
15
det(M) = (10 × 5) − (5 × 7) = 50 − 35 = 15.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [3, 3]].
9
det(M) = (7 × 3) − (4 × 3) = 21 − 12 = 9.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [2, 7]].
38
det(M) = (6 × 7) − (2 × 2) = 42 − 4 = 38.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [5, 4]].
24
det(M) = (11 × 4) − (4 × 5) = 44 − 20 = 24.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [3, 4]].
20
det(M) = (11 × 4) − (8 × 3) = 44 − 24 = 20.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 10], [2, 5]].
5
det(M) = (5 × 5) − (10 × 2) = 25 − 20 = 5.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [6, 6]].
0
det(M) = (7 × 6) − (7 × 6) = 42 − 42 = 0.

12 questions · Seed 104743 · 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 = [[9, 7], [1, 2]].
M = [ 9 7 ; 1 2 ] · det(M) = (9×2) − (7×1)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [2, 4]].
M = [ 2 7 ; 2 4 ] · det(M) = (2×4) − (7×2)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [2, 7]].
M = [ 10 2 ; 2 7 ] · det(M) = (10×7) − (2×2)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [10, 12]].
M = [ 5 5 ; 10 12 ] · det(M) = (5×12) − (5×10)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [4, 2]].
M = [ 11 7 ; 4 2 ] · det(M) = (11×2) − (7×4)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [7, 5]].
M = [ 10 5 ; 7 5 ] · det(M) = (10×5) − (5×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [3, 3]].
M = [ 7 4 ; 3 3 ] · det(M) = (7×3) − (4×3)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [2, 7]].
M = [ 6 2 ; 2 7 ] · det(M) = (6×7) − (2×2)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [5, 4]].
M = [ 11 4 ; 5 4 ] · det(M) = (11×4) − (4×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [3, 4]].
M = [ 11 8 ; 3 4 ] · det(M) = (11×4) − (8×3)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 10], [2, 5]].
M = [ 5 10 ; 2 5 ] · det(M) = (5×5) − (10×2)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [6, 6]].
M = [ 7 7 ; 6 6 ] · det(M) = (7×6) − (7×6)

12 questions · Seed 104743 · 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 = [[9, 7], [1, 2]].
11
det(M) = (9 × 2) − (7 × 1) = 18 − 7 = 11.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [2, 4]].
-6
det(M) = (2 × 4) − (7 × 2) = 8 − 14 = -6.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [2, 7]].
66
det(M) = (10 × 7) − (2 × 2) = 70 − 4 = 66.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [10, 12]].
10
det(M) = (5 × 12) − (5 × 10) = 60 − 50 = 10.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [4, 2]].
-6
det(M) = (11 × 2) − (7 × 4) = 22 − 28 = -6.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [7, 5]].
15
det(M) = (10 × 5) − (5 × 7) = 50 − 35 = 15.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [3, 3]].
9
det(M) = (7 × 3) − (4 × 3) = 21 − 12 = 9.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [2, 7]].
38
det(M) = (6 × 7) − (2 × 2) = 42 − 4 = 38.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [5, 4]].
24
det(M) = (11 × 4) − (4 × 5) = 44 − 20 = 24.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [3, 4]].
20
det(M) = (11 × 4) − (8 × 3) = 44 − 24 = 20.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 10], [2, 5]].
5
det(M) = (5 × 5) − (10 × 2) = 25 − 20 = 5.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [6, 6]].
0
det(M) = (7 × 6) − (7 × 6) = 42 − 42 = 0.

12 questions · Seed 104743 · Age guidance, not curriculum certification