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

12 questions · Seed 58 · 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 = [[2, 7], [5, 10]].
-15
det(M) = (2 × 10) − (7 × 5) = 20 − 35 = -15.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [8, 2]].
-20
det(M) = (2 × 2) − (3 × 8) = 4 − 24 = -20.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [8, 9]].
13
det(M) = (5 × 9) − (4 × 8) = 45 − 32 = 13.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [9, 12]].
3
det(M) = (4 × 12) − (5 × 9) = 48 − 45 = 3.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [4, 7]].
44
det(M) = (8 × 7) − (3 × 4) = 56 − 12 = 44.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [7, 10]].
55
det(M) = (9 × 10) − (5 × 7) = 90 − 35 = 55.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [9, 8]].
17
det(M) = (10 × 8) − (7 × 9) = 80 − 63 = 17.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [1, 5]].
31
det(M) = (8 × 5) − (9 × 1) = 40 − 9 = 31.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [2, 5]].
8
det(M) = (4 × 5) − (6 × 2) = 20 − 12 = 8.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [1, 8]].
70
det(M) = (9 × 8) − (2 × 1) = 72 − 2 = 70.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [1, 7]].
32
det(M) = (5 × 7) − (3 × 1) = 35 − 3 = 32.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [9, 9]].
-27
det(M) = (6 × 9) − (9 × 9) = 54 − 81 = -27.

12 questions · Seed 58 · 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 = [[2, 7], [5, 10]].
M = [ 2 7 ; 5 10 ] · det(M) = (2×10) − (7×5)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [8, 2]].
M = [ 2 3 ; 8 2 ] · det(M) = (2×2) − (3×8)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [8, 9]].
M = [ 5 4 ; 8 9 ] · det(M) = (5×9) − (4×8)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [9, 12]].
M = [ 4 5 ; 9 12 ] · det(M) = (4×12) − (5×9)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [4, 7]].
M = [ 8 3 ; 4 7 ] · det(M) = (8×7) − (3×4)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [7, 10]].
M = [ 9 5 ; 7 10 ] · det(M) = (9×10) − (5×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [9, 8]].
M = [ 10 7 ; 9 8 ] · det(M) = (10×8) − (7×9)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [1, 5]].
M = [ 8 9 ; 1 5 ] · det(M) = (8×5) − (9×1)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [2, 5]].
M = [ 4 6 ; 2 5 ] · det(M) = (4×5) − (6×2)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [1, 8]].
M = [ 9 2 ; 1 8 ] · det(M) = (9×8) − (2×1)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [1, 7]].
M = [ 5 3 ; 1 7 ] · det(M) = (5×7) − (3×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [9, 9]].
M = [ 6 9 ; 9 9 ] · det(M) = (6×9) − (9×9)

12 questions · Seed 58 · 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 = [[2, 7], [5, 10]].
-15
det(M) = (2 × 10) − (7 × 5) = 20 − 35 = -15.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [8, 2]].
-20
det(M) = (2 × 2) − (3 × 8) = 4 − 24 = -20.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [8, 9]].
13
det(M) = (5 × 9) − (4 × 8) = 45 − 32 = 13.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [9, 12]].
3
det(M) = (4 × 12) − (5 × 9) = 48 − 45 = 3.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [4, 7]].
44
det(M) = (8 × 7) − (3 × 4) = 56 − 12 = 44.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [7, 10]].
55
det(M) = (9 × 10) − (5 × 7) = 90 − 35 = 55.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [9, 8]].
17
det(M) = (10 × 8) − (7 × 9) = 80 − 63 = 17.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [1, 5]].
31
det(M) = (8 × 5) − (9 × 1) = 40 − 9 = 31.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [2, 5]].
8
det(M) = (4 × 5) − (6 × 2) = 20 − 12 = 8.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [1, 8]].
70
det(M) = (9 × 8) − (2 × 1) = 72 − 2 = 70.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [1, 7]].
32
det(M) = (5 × 7) − (3 × 1) = 35 − 3 = 32.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [9, 9]].
-27
det(M) = (6 × 9) − (9 × 9) = 54 − 81 = -27.

12 questions · Seed 58 · Age guidance, not curriculum certification