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

12 questions · Seed 104745 · 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 = [[12, 6], [3, 10]].
102
det(M) = (12 × 10) − (6 × 3) = 120 − 18 = 102.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [7, 5]].
-32
det(M) = (2 × 5) − (6 × 7) = 10 − 42 = -32.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [9, 9]].
-9
det(M) = (2 × 9) − (3 × 9) = 18 − 27 = -9.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 10]].
35
det(M) = (5 × 10) − (5 × 3) = 50 − 15 = 35.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [6, 10]].
24
det(M) = (3 × 10) − (1 × 6) = 30 − 6 = 24.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [1, 9]].
11
det(M) = (2 × 9) − (7 × 1) = 18 − 7 = 11.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [5, 11]].
87
det(M) = (12 × 11) − (9 × 5) = 132 − 45 = 87.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [10, 5]].
-55
det(M) = (9 × 5) − (10 × 10) = 45 − 100 = -55.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [8, 5]].
17
det(M) = (5 × 5) − (1 × 8) = 25 − 8 = 17.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [3, 7]].
11
det(M) = (2 × 7) − (1 × 3) = 14 − 3 = 11.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [1, 2]].
3
det(M) = (5 × 2) − (7 × 1) = 10 − 7 = 3.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [2, 11]].
112
det(M) = (12 × 11) − (10 × 2) = 132 − 20 = 112.

12 questions · Seed 104745 · 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 = [[12, 6], [3, 10]].
M = [ 12 6 ; 3 10 ] · det(M) = (12×10) − (6×3)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [7, 5]].
M = [ 2 6 ; 7 5 ] · det(M) = (2×5) − (6×7)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [9, 9]].
M = [ 2 3 ; 9 9 ] · det(M) = (2×9) − (3×9)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 10]].
M = [ 5 5 ; 3 10 ] · det(M) = (5×10) − (5×3)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [6, 10]].
M = [ 3 1 ; 6 10 ] · det(M) = (3×10) − (1×6)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [1, 9]].
M = [ 2 7 ; 1 9 ] · det(M) = (2×9) − (7×1)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [5, 11]].
M = [ 12 9 ; 5 11 ] · det(M) = (12×11) − (9×5)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [10, 5]].
M = [ 9 10 ; 10 5 ] · det(M) = (9×5) − (10×10)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [8, 5]].
M = [ 5 1 ; 8 5 ] · det(M) = (5×5) − (1×8)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [3, 7]].
M = [ 2 1 ; 3 7 ] · det(M) = (2×7) − (1×3)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [1, 2]].
M = [ 5 7 ; 1 2 ] · det(M) = (5×2) − (7×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [2, 11]].
M = [ 12 10 ; 2 11 ] · det(M) = (12×11) − (10×2)

12 questions · Seed 104745 · 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 = [[12, 6], [3, 10]].
102
det(M) = (12 × 10) − (6 × 3) = 120 − 18 = 102.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [7, 5]].
-32
det(M) = (2 × 5) − (6 × 7) = 10 − 42 = -32.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [9, 9]].
-9
det(M) = (2 × 9) − (3 × 9) = 18 − 27 = -9.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 10]].
35
det(M) = (5 × 10) − (5 × 3) = 50 − 15 = 35.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [6, 10]].
24
det(M) = (3 × 10) − (1 × 6) = 30 − 6 = 24.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [1, 9]].
11
det(M) = (2 × 9) − (7 × 1) = 18 − 7 = 11.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [5, 11]].
87
det(M) = (12 × 11) − (9 × 5) = 132 − 45 = 87.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [10, 5]].
-55
det(M) = (9 × 5) − (10 × 10) = 45 − 100 = -55.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [8, 5]].
17
det(M) = (5 × 5) − (1 × 8) = 25 − 8 = 17.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [3, 7]].
11
det(M) = (2 × 7) − (1 × 3) = 14 − 3 = 11.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [1, 2]].
3
det(M) = (5 × 2) − (7 × 1) = 10 − 7 = 3.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [2, 11]].
112
det(M) = (12 × 11) − (10 × 2) = 132 − 20 = 112.

12 questions · Seed 104745 · Age guidance, not curriculum certification