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

12 questions · Seed 43 · 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 = [[11, 10], [9, 3]].
-57
det(M) = (11 × 3) − (10 × 9) = 33 − 90 = -57.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [10, 4]].
16
det(M) = (9 × 4) − (2 × 10) = 36 − 20 = 16.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [5, 8]].
63
det(M) = (11 × 8) − (5 × 5) = 88 − 25 = 63.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [6, 6]].
18
det(M) = (7 × 6) − (4 × 6) = 42 − 24 = 18.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [2, 10]].
106
det(M) = (11 × 10) − (2 × 2) = 110 − 4 = 106.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [9, 10]].
22
det(M) = (4 × 10) − (2 × 9) = 40 − 18 = 22.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [2, 7]].
17
det(M) = (3 × 7) − (2 × 2) = 21 − 4 = 17.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [7, 3]].
11
det(M) = (6 × 3) − (1 × 7) = 18 − 7 = 11.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [8, 7]].
-20
det(M) = (4 × 7) − (6 × 8) = 28 − 48 = -20.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [9, 12]].
105
det(M) = (11 × 12) − (3 × 9) = 132 − 27 = 105.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [10, 2]].
-16
det(M) = (2 × 2) − (2 × 10) = 4 − 20 = -16.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [4, 4]].
-4
det(M) = (2 × 4) − (3 × 4) = 8 − 12 = -4.

12 questions · Seed 43 · 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 = [[11, 10], [9, 3]].
M = [ 11 10 ; 9 3 ] · det(M) = (11×3) − (10×9)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [10, 4]].
M = [ 9 2 ; 10 4 ] · det(M) = (9×4) − (2×10)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [5, 8]].
M = [ 11 5 ; 5 8 ] · det(M) = (11×8) − (5×5)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [6, 6]].
M = [ 7 4 ; 6 6 ] · det(M) = (7×6) − (4×6)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [2, 10]].
M = [ 11 2 ; 2 10 ] · det(M) = (11×10) − (2×2)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [9, 10]].
M = [ 4 2 ; 9 10 ] · det(M) = (4×10) − (2×9)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [2, 7]].
M = [ 3 2 ; 2 7 ] · det(M) = (3×7) − (2×2)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [7, 3]].
M = [ 6 1 ; 7 3 ] · det(M) = (6×3) − (1×7)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [8, 7]].
M = [ 4 6 ; 8 7 ] · det(M) = (4×7) − (6×8)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [9, 12]].
M = [ 11 3 ; 9 12 ] · det(M) = (11×12) − (3×9)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [10, 2]].
M = [ 2 2 ; 10 2 ] · det(M) = (2×2) − (2×10)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [4, 4]].
M = [ 2 3 ; 4 4 ] · det(M) = (2×4) − (3×4)

12 questions · Seed 43 · 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 = [[11, 10], [9, 3]].
-57
det(M) = (11 × 3) − (10 × 9) = 33 − 90 = -57.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [10, 4]].
16
det(M) = (9 × 4) − (2 × 10) = 36 − 20 = 16.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [5, 8]].
63
det(M) = (11 × 8) − (5 × 5) = 88 − 25 = 63.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [6, 6]].
18
det(M) = (7 × 6) − (4 × 6) = 42 − 24 = 18.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [2, 10]].
106
det(M) = (11 × 10) − (2 × 2) = 110 − 4 = 106.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [9, 10]].
22
det(M) = (4 × 10) − (2 × 9) = 40 − 18 = 22.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [2, 7]].
17
det(M) = (3 × 7) − (2 × 2) = 21 − 4 = 17.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [7, 3]].
11
det(M) = (6 × 3) − (1 × 7) = 18 − 7 = 11.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [8, 7]].
-20
det(M) = (4 × 7) − (6 × 8) = 28 − 48 = -20.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [9, 12]].
105
det(M) = (11 × 12) − (3 × 9) = 132 − 27 = 105.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [10, 2]].
-16
det(M) = (2 × 2) − (2 × 10) = 4 − 20 = -16.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [4, 4]].
-4
det(M) = (2 × 4) − (3 × 4) = 8 − 12 = -4.

12 questions · Seed 43 · Age guidance, not curriculum certification