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

12 questions · Seed 104742 · 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, 1], [7, 12]].
137
det(M) = (12 × 12) − (1 × 7) = 144 − 7 = 137.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [6, 12]].
0
det(M) = (2 × 12) − (4 × 6) = 24 − 24 = 0.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 9], [2, 11]].
15
det(M) = (3 × 11) − (9 × 2) = 33 − 18 = 15.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [9, 10]].
-70
det(M) = (2 × 10) − (10 × 9) = 20 − 90 = -70.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [6, 11]].
27
det(M) = (3 × 11) − (1 × 6) = 33 − 6 = 27.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [10, 3]].
-24
det(M) = (12 × 3) − (6 × 10) = 36 − 60 = -24.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [3, 7]].
32
det(M) = (5 × 7) − (1 × 3) = 35 − 3 = 32.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [8, 6]].
18
det(M) = (7 × 6) − (3 × 8) = 42 − 24 = 18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [9, 10]].
102
det(M) = (12 × 10) − (2 × 9) = 120 − 18 = 102.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [7, 2]].
-27
det(M) = (11 × 2) − (7 × 7) = 22 − 49 = -27.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [6, 10]].
38
det(M) = (5 × 10) − (2 × 6) = 50 − 12 = 38.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [1, 10]].
18
det(M) = (2 × 10) − (2 × 1) = 20 − 2 = 18.

12 questions · Seed 104742 · 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, 1], [7, 12]].
M = [ 12 1 ; 7 12 ] · det(M) = (12×12) − (1×7)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [6, 12]].
M = [ 2 4 ; 6 12 ] · det(M) = (2×12) − (4×6)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 9], [2, 11]].
M = [ 3 9 ; 2 11 ] · det(M) = (3×11) − (9×2)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [9, 10]].
M = [ 2 10 ; 9 10 ] · det(M) = (2×10) − (10×9)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [6, 11]].
M = [ 3 1 ; 6 11 ] · det(M) = (3×11) − (1×6)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [10, 3]].
M = [ 12 6 ; 10 3 ] · det(M) = (12×3) − (6×10)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [3, 7]].
M = [ 5 1 ; 3 7 ] · det(M) = (5×7) − (1×3)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [8, 6]].
M = [ 7 3 ; 8 6 ] · det(M) = (7×6) − (3×8)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [9, 10]].
M = [ 12 2 ; 9 10 ] · det(M) = (12×10) − (2×9)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [7, 2]].
M = [ 11 7 ; 7 2 ] · det(M) = (11×2) − (7×7)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [6, 10]].
M = [ 5 2 ; 6 10 ] · det(M) = (5×10) − (2×6)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [1, 10]].
M = [ 2 2 ; 1 10 ] · det(M) = (2×10) − (2×1)

12 questions · Seed 104742 · 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, 1], [7, 12]].
137
det(M) = (12 × 12) − (1 × 7) = 144 − 7 = 137.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [6, 12]].
0
det(M) = (2 × 12) − (4 × 6) = 24 − 24 = 0.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 9], [2, 11]].
15
det(M) = (3 × 11) − (9 × 2) = 33 − 18 = 15.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [9, 10]].
-70
det(M) = (2 × 10) − (10 × 9) = 20 − 90 = -70.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [6, 11]].
27
det(M) = (3 × 11) − (1 × 6) = 33 − 6 = 27.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [10, 3]].
-24
det(M) = (12 × 3) − (6 × 10) = 36 − 60 = -24.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [3, 7]].
32
det(M) = (5 × 7) − (1 × 3) = 35 − 3 = 32.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [8, 6]].
18
det(M) = (7 × 6) − (3 × 8) = 42 − 24 = 18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [9, 10]].
102
det(M) = (12 × 10) − (2 × 9) = 120 − 18 = 102.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [7, 2]].
-27
det(M) = (11 × 2) − (7 × 7) = 22 − 49 = -27.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [6, 10]].
38
det(M) = (5 × 10) − (2 × 6) = 50 − 12 = 38.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [1, 10]].
18
det(M) = (2 × 10) − (2 × 1) = 20 − 2 = 18.

12 questions · Seed 104742 · Age guidance, not curriculum certification