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

12 questions · Seed 104732 · 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, 2], [5, 8]].
22
det(M) = (4 × 8) − (2 × 5) = 32 − 10 = 22.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [3, 7]].
12
det(M) = (6 × 7) − (10 × 3) = 42 − 30 = 12.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [1, 3]].
9
det(M) = (4 × 3) − (3 × 1) = 12 − 3 = 9.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [2, 9]].
37
det(M) = (5 × 9) − (4 × 2) = 45 − 8 = 37.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 5], [8, 5]].
-10
det(M) = (6 × 5) − (5 × 8) = 30 − 40 = -10.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [1, 8]].
53
det(M) = (7 × 8) − (3 × 1) = 56 − 3 = 53.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [2, 11]].
40
det(M) = (4 × 11) − (2 × 2) = 44 − 4 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [2, 7]].
0
det(M) = (2 × 7) − (7 × 2) = 14 − 14 = 0.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
-36
det(M) = (2 × 2) − (4 × 10) = 4 − 40 = -36.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 10], [7, 2]].
-56
det(M) = (7 × 2) − (10 × 7) = 14 − 70 = -56.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 3], [9, 11]].
39
det(M) = (6 × 11) − (3 × 9) = 66 − 27 = 39.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [10, 9]].
31
det(M) = (9 × 9) − (5 × 10) = 81 − 50 = 31.

12 questions · Seed 104732 · 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, 2], [5, 8]].
M = [ 4 2 ; 5 8 ] · det(M) = (4×8) − (2×5)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [3, 7]].
M = [ 6 10 ; 3 7 ] · det(M) = (6×7) − (10×3)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [1, 3]].
M = [ 4 3 ; 1 3 ] · det(M) = (4×3) − (3×1)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [2, 9]].
M = [ 5 4 ; 2 9 ] · det(M) = (5×9) − (4×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 5], [8, 5]].
M = [ 6 5 ; 8 5 ] · det(M) = (6×5) − (5×8)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [1, 8]].
M = [ 7 3 ; 1 8 ] · det(M) = (7×8) − (3×1)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [2, 11]].
M = [ 4 2 ; 2 11 ] · det(M) = (4×11) − (2×2)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [2, 7]].
M = [ 2 7 ; 2 7 ] · det(M) = (2×7) − (7×2)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
M = [ 2 4 ; 10 2 ] · det(M) = (2×2) − (4×10)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 10], [7, 2]].
M = [ 7 10 ; 7 2 ] · det(M) = (7×2) − (10×7)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 3], [9, 11]].
M = [ 6 3 ; 9 11 ] · det(M) = (6×11) − (3×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [10, 9]].
M = [ 9 5 ; 10 9 ] · det(M) = (9×9) − (5×10)

12 questions · Seed 104732 · 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, 2], [5, 8]].
22
det(M) = (4 × 8) − (2 × 5) = 32 − 10 = 22.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [3, 7]].
12
det(M) = (6 × 7) − (10 × 3) = 42 − 30 = 12.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [1, 3]].
9
det(M) = (4 × 3) − (3 × 1) = 12 − 3 = 9.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [2, 9]].
37
det(M) = (5 × 9) − (4 × 2) = 45 − 8 = 37.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 5], [8, 5]].
-10
det(M) = (6 × 5) − (5 × 8) = 30 − 40 = -10.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [1, 8]].
53
det(M) = (7 × 8) − (3 × 1) = 56 − 3 = 53.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [2, 11]].
40
det(M) = (4 × 11) − (2 × 2) = 44 − 4 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [2, 7]].
0
det(M) = (2 × 7) − (7 × 2) = 14 − 14 = 0.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
-36
det(M) = (2 × 2) − (4 × 10) = 4 − 40 = -36.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 10], [7, 2]].
-56
det(M) = (7 × 2) − (10 × 7) = 14 − 70 = -56.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 3], [9, 11]].
39
det(M) = (6 × 11) − (3 × 9) = 66 − 27 = 39.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [10, 9]].
31
det(M) = (9 × 9) − (5 × 10) = 81 − 50 = 31.

12 questions · Seed 104732 · Age guidance, not curriculum certification