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

12 questions · Seed 62 · 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, 3], [4, 3]].
-3
det(M) = (3 × 3) − (3 × 4) = 9 − 12 = -3.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 3]].
-20
det(M) = (5 × 3) − (5 × 7) = 15 − 35 = -20.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [1, 7]].
15
det(M) = (3 × 7) − (6 × 1) = 21 − 6 = 15.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [2, 3]].
10
det(M) = (4 × 3) − (1 × 2) = 12 − 2 = 10.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [4, 7]].
1
det(M) = (3 × 7) − (5 × 4) = 21 − 20 = 1.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [3, 5]].
25
det(M) = (8 × 5) − (5 × 3) = 40 − 15 = 25.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [9, 6]].
-36
det(M) = (6 × 6) − (8 × 9) = 36 − 72 = -36.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [3, 7]].
37
det(M) = (7 × 7) − (4 × 3) = 49 − 12 = 37.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [5, 11]].
32
det(M) = (7 × 11) − (9 × 5) = 77 − 45 = 32.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [5, 12]].
61
det(M) = (8 × 12) − (7 × 5) = 96 − 35 = 61.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [6, 10]].
4
det(M) = (4 × 10) − (6 × 6) = 40 − 36 = 4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [1, 8]].
61
det(M) = (8 × 8) − (3 × 1) = 64 − 3 = 61.

12 questions · Seed 62 · 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, 3], [4, 3]].
M = [ 3 3 ; 4 3 ] · det(M) = (3×3) − (3×4)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 3]].
M = [ 5 5 ; 7 3 ] · det(M) = (5×3) − (5×7)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [1, 7]].
M = [ 3 6 ; 1 7 ] · det(M) = (3×7) − (6×1)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [2, 3]].
M = [ 4 1 ; 2 3 ] · det(M) = (4×3) − (1×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [4, 7]].
M = [ 3 5 ; 4 7 ] · det(M) = (3×7) − (5×4)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [3, 5]].
M = [ 8 5 ; 3 5 ] · det(M) = (8×5) − (5×3)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [9, 6]].
M = [ 6 8 ; 9 6 ] · det(M) = (6×6) − (8×9)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [3, 7]].
M = [ 7 4 ; 3 7 ] · det(M) = (7×7) − (4×3)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [5, 11]].
M = [ 7 9 ; 5 11 ] · det(M) = (7×11) − (9×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [5, 12]].
M = [ 8 7 ; 5 12 ] · det(M) = (8×12) − (7×5)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [6, 10]].
M = [ 4 6 ; 6 10 ] · det(M) = (4×10) − (6×6)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [1, 8]].
M = [ 8 3 ; 1 8 ] · det(M) = (8×8) − (3×1)

12 questions · Seed 62 · 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, 3], [4, 3]].
-3
det(M) = (3 × 3) − (3 × 4) = 9 − 12 = -3.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 3]].
-20
det(M) = (5 × 3) − (5 × 7) = 15 − 35 = -20.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [1, 7]].
15
det(M) = (3 × 7) − (6 × 1) = 21 − 6 = 15.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [2, 3]].
10
det(M) = (4 × 3) − (1 × 2) = 12 − 2 = 10.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [4, 7]].
1
det(M) = (3 × 7) − (5 × 4) = 21 − 20 = 1.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [3, 5]].
25
det(M) = (8 × 5) − (5 × 3) = 40 − 15 = 25.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [9, 6]].
-36
det(M) = (6 × 6) − (8 × 9) = 36 − 72 = -36.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 4], [3, 7]].
37
det(M) = (7 × 7) − (4 × 3) = 49 − 12 = 37.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [5, 11]].
32
det(M) = (7 × 11) − (9 × 5) = 77 − 45 = 32.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [5, 12]].
61
det(M) = (8 × 12) − (7 × 5) = 96 − 35 = 61.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [6, 10]].
4
det(M) = (4 × 10) − (6 × 6) = 40 − 36 = 4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [1, 8]].
61
det(M) = (8 × 8) − (3 × 1) = 64 − 3 = 61.

12 questions · Seed 62 · Age guidance, not curriculum certification