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

12 questions · Seed 49 · 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 = [[4, 7], [1, 2]].
1
det(M) = (4 × 2) − (7 × 1) = 8 − 7 = 1.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [2, 4]].
28
det(M) = (12 × 4) − (10 × 2) = 48 − 20 = 28.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [10, 10]].
-80
det(M) = (2 × 10) − (10 × 10) = 20 − 100 = -80.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [6, 10]].
70
det(M) = (10 × 10) − (5 × 6) = 100 − 30 = 70.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [1, 4]].
12
det(M) = (5 × 4) − (8 × 1) = 20 − 8 = 12.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [10, 6]].
-22
det(M) = (3 × 6) − (4 × 10) = 18 − 40 = -22.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 10], [7, 8]].
-30
det(M) = (5 × 8) − (10 × 7) = 40 − 70 = -30.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [3, 11]].
39
det(M) = (6 × 11) − (9 × 3) = 66 − 27 = 39.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [5, 7]].
20
det(M) = (5 × 7) − (3 × 5) = 35 − 15 = 20.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [9, 11]].
-28
det(M) = (4 × 11) − (8 × 9) = 44 − 72 = -28.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [8, 5]].
-46
det(M) = (2 × 5) − (7 × 8) = 10 − 56 = -46.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 5], [8, 3]].
-22
det(M) = (6 × 3) − (5 × 8) = 18 − 40 = -22.

12 questions · Seed 49 · 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 = [[4, 7], [1, 2]].
M = [ 4 7 ; 1 2 ] · det(M) = (4×2) − (7×1)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [2, 4]].
M = [ 12 10 ; 2 4 ] · det(M) = (12×4) − (10×2)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [10, 10]].
M = [ 2 10 ; 10 10 ] · det(M) = (2×10) − (10×10)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [6, 10]].
M = [ 10 5 ; 6 10 ] · det(M) = (10×10) − (5×6)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [1, 4]].
M = [ 5 8 ; 1 4 ] · det(M) = (5×4) − (8×1)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [10, 6]].
M = [ 3 4 ; 10 6 ] · det(M) = (3×6) − (4×10)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 10], [7, 8]].
M = [ 5 10 ; 7 8 ] · det(M) = (5×8) − (10×7)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [3, 11]].
M = [ 6 9 ; 3 11 ] · det(M) = (6×11) − (9×3)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [5, 7]].
M = [ 5 3 ; 5 7 ] · det(M) = (5×7) − (3×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [9, 11]].
M = [ 4 8 ; 9 11 ] · det(M) = (4×11) − (8×9)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [8, 5]].
M = [ 2 7 ; 8 5 ] · det(M) = (2×5) − (7×8)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 5], [8, 3]].
M = [ 6 5 ; 8 3 ] · det(M) = (6×3) − (5×8)

12 questions · Seed 49 · 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 = [[4, 7], [1, 2]].
1
det(M) = (4 × 2) − (7 × 1) = 8 − 7 = 1.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [2, 4]].
28
det(M) = (12 × 4) − (10 × 2) = 48 − 20 = 28.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [10, 10]].
-80
det(M) = (2 × 10) − (10 × 10) = 20 − 100 = -80.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [6, 10]].
70
det(M) = (10 × 10) − (5 × 6) = 100 − 30 = 70.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [1, 4]].
12
det(M) = (5 × 4) − (8 × 1) = 20 − 8 = 12.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [10, 6]].
-22
det(M) = (3 × 6) − (4 × 10) = 18 − 40 = -22.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 10], [7, 8]].
-30
det(M) = (5 × 8) − (10 × 7) = 40 − 70 = -30.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [3, 11]].
39
det(M) = (6 × 11) − (9 × 3) = 66 − 27 = 39.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [5, 7]].
20
det(M) = (5 × 7) − (3 × 5) = 35 − 15 = 20.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [9, 11]].
-28
det(M) = (4 × 11) − (8 × 9) = 44 − 72 = -28.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [8, 5]].
-46
det(M) = (2 × 5) − (7 × 8) = 10 − 56 = -46.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 5], [8, 3]].
-22
det(M) = (6 × 3) − (5 × 8) = 18 − 40 = -22.

12 questions · Seed 49 · Age guidance, not curriculum certification