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

12 questions · Seed 104735 · 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 = [[3, 9], [3, 6]].
-9
det(M) = (3 × 6) − (9 × 3) = 18 − 27 = -9.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 6], [3, 12]].
78
det(M) = (8 × 12) − (6 × 3) = 96 − 18 = 78.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [5, 9]].
0
det(M) = (5 × 9) − (9 × 5) = 45 − 45 = 0.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [6, 11]].
-2
det(M) = (2 × 11) − (4 × 6) = 22 − 24 = -2.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [8, 5]].
39
det(M) = (11 × 5) − (2 × 8) = 55 − 16 = 39.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [7, 12]].
-8
det(M) = (4 × 12) − (8 × 7) = 48 − 56 = -8.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [4, 10]].
10
det(M) = (3 × 10) − (5 × 4) = 30 − 20 = 10.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [2, 6]].
18
det(M) = (4 × 6) − (3 × 2) = 24 − 6 = 18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [1, 10]].
48
det(M) = (5 × 10) − (2 × 1) = 50 − 2 = 48.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [9, 4]].
8
det(M) = (11 × 4) − (4 × 9) = 44 − 36 = 8.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [1, 11]].
30
det(M) = (3 × 11) − (3 × 1) = 33 − 3 = 30.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 10]].
8
det(M) = (4 × 10) − (8 × 4) = 40 − 32 = 8.

12 questions · Seed 104735 · 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 = [[3, 9], [3, 6]].
M = [ 3 9 ; 3 6 ] · det(M) = (3×6) − (9×3)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 6], [3, 12]].
M = [ 8 6 ; 3 12 ] · det(M) = (8×12) − (6×3)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [5, 9]].
M = [ 5 9 ; 5 9 ] · det(M) = (5×9) − (9×5)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [6, 11]].
M = [ 2 4 ; 6 11 ] · det(M) = (2×11) − (4×6)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [8, 5]].
M = [ 11 2 ; 8 5 ] · det(M) = (11×5) − (2×8)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [7, 12]].
M = [ 4 8 ; 7 12 ] · det(M) = (4×12) − (8×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [4, 10]].
M = [ 3 5 ; 4 10 ] · det(M) = (3×10) − (5×4)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [2, 6]].
M = [ 4 3 ; 2 6 ] · det(M) = (4×6) − (3×2)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [1, 10]].
M = [ 5 2 ; 1 10 ] · det(M) = (5×10) − (2×1)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [9, 4]].
M = [ 11 4 ; 9 4 ] · det(M) = (11×4) − (4×9)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [1, 11]].
M = [ 3 3 ; 1 11 ] · det(M) = (3×11) − (3×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 10]].
M = [ 4 8 ; 4 10 ] · det(M) = (4×10) − (8×4)

12 questions · Seed 104735 · 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 = [[3, 9], [3, 6]].
-9
det(M) = (3 × 6) − (9 × 3) = 18 − 27 = -9.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 6], [3, 12]].
78
det(M) = (8 × 12) − (6 × 3) = 96 − 18 = 78.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [5, 9]].
0
det(M) = (5 × 9) − (9 × 5) = 45 − 45 = 0.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [6, 11]].
-2
det(M) = (2 × 11) − (4 × 6) = 22 − 24 = -2.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [8, 5]].
39
det(M) = (11 × 5) − (2 × 8) = 55 − 16 = 39.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [7, 12]].
-8
det(M) = (4 × 12) − (8 × 7) = 48 − 56 = -8.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [4, 10]].
10
det(M) = (3 × 10) − (5 × 4) = 30 − 20 = 10.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [2, 6]].
18
det(M) = (4 × 6) − (3 × 2) = 24 − 6 = 18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [1, 10]].
48
det(M) = (5 × 10) − (2 × 1) = 50 − 2 = 48.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [9, 4]].
8
det(M) = (11 × 4) − (4 × 9) = 44 − 36 = 8.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [1, 11]].
30
det(M) = (3 × 11) − (3 × 1) = 33 − 3 = 30.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 10]].
8
det(M) = (4 × 10) − (8 × 4) = 40 − 32 = 8.

12 questions · Seed 104735 · Age guidance, not curriculum certification