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

12 questions · Seed 104746 · 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 = [[6, 4], [2, 9]].
46
det(M) = (6 × 9) − (4 × 2) = 54 − 8 = 46.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [4, 8]].
52
det(M) = (10 × 8) − (7 × 4) = 80 − 28 = 52.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 12]].
16
det(M) = (3 × 12) − (4 × 5) = 36 − 20 = 16.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [10, 5]].
-25
det(M) = (5 × 5) − (5 × 10) = 25 − 50 = -25.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [6, 10]].
108
det(M) = (12 × 10) − (2 × 6) = 120 − 12 = 108.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [10, 6]].
-14
det(M) = (11 × 6) − (8 × 10) = 66 − 80 = -14.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [7, 6]].
2
det(M) = (5 × 6) − (4 × 7) = 30 − 28 = 2.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [7, 2]].
-18
det(M) = (5 × 2) − (4 × 7) = 10 − 28 = -18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [10, 2]].
-56
det(M) = (7 × 2) − (7 × 10) = 14 − 70 = -56.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [9, 6]].
-30
det(M) = (4 × 6) − (6 × 9) = 24 − 54 = -30.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [1, 4]].
18
det(M) = (5 × 4) − (2 × 1) = 20 − 2 = 18.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 5], [2, 3]].
11
det(M) = (7 × 3) − (5 × 2) = 21 − 10 = 11.

12 questions · Seed 104746 · 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 = [[6, 4], [2, 9]].
M = [ 6 4 ; 2 9 ] · det(M) = (6×9) − (4×2)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [4, 8]].
M = [ 10 7 ; 4 8 ] · det(M) = (10×8) − (7×4)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 12]].
M = [ 3 4 ; 5 12 ] · det(M) = (3×12) − (4×5)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [10, 5]].
M = [ 5 5 ; 10 5 ] · det(M) = (5×5) − (5×10)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [6, 10]].
M = [ 12 2 ; 6 10 ] · det(M) = (12×10) − (2×6)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [10, 6]].
M = [ 11 8 ; 10 6 ] · det(M) = (11×6) − (8×10)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [7, 6]].
M = [ 5 4 ; 7 6 ] · det(M) = (5×6) − (4×7)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [7, 2]].
M = [ 5 4 ; 7 2 ] · det(M) = (5×2) − (4×7)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [10, 2]].
M = [ 7 7 ; 10 2 ] · det(M) = (7×2) − (7×10)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [9, 6]].
M = [ 4 6 ; 9 6 ] · det(M) = (4×6) − (6×9)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [1, 4]].
M = [ 5 2 ; 1 4 ] · det(M) = (5×4) − (2×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 5], [2, 3]].
M = [ 7 5 ; 2 3 ] · det(M) = (7×3) − (5×2)

12 questions · Seed 104746 · 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 = [[6, 4], [2, 9]].
46
det(M) = (6 × 9) − (4 × 2) = 54 − 8 = 46.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [4, 8]].
52
det(M) = (10 × 8) − (7 × 4) = 80 − 28 = 52.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 12]].
16
det(M) = (3 × 12) − (4 × 5) = 36 − 20 = 16.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [10, 5]].
-25
det(M) = (5 × 5) − (5 × 10) = 25 − 50 = -25.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [6, 10]].
108
det(M) = (12 × 10) − (2 × 6) = 120 − 12 = 108.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [10, 6]].
-14
det(M) = (11 × 6) − (8 × 10) = 66 − 80 = -14.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [7, 6]].
2
det(M) = (5 × 6) − (4 × 7) = 30 − 28 = 2.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [7, 2]].
-18
det(M) = (5 × 2) − (4 × 7) = 10 − 28 = -18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [10, 2]].
-56
det(M) = (7 × 2) − (7 × 10) = 14 − 70 = -56.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [9, 6]].
-30
det(M) = (4 × 6) − (6 × 9) = 24 − 54 = -30.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [1, 4]].
18
det(M) = (5 × 4) − (2 × 1) = 20 − 2 = 18.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 5], [2, 3]].
11
det(M) = (7 × 3) − (5 × 2) = 21 − 10 = 11.

12 questions · Seed 104746 · Age guidance, not curriculum certification