Matrices
3 × 3 determinant worksheets
Evaluate twelve determinants of 3 × 3 matrices with numeric, algebraic or mixed entries. Algebraic questions supply one variable value for the final numeric answer.
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2 × 2 determinant worksheets
Evaluate twelve determinants of 2 × 2 matrices with numeric, algebraic or mixed entries. Algebraic questions supply one variable value for the final numeric answer.
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On an algebraic question, substitute the given value into the matrix first. Then, for entries a, b, c and d read by rows, calculate ad − bc exactly.
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Customize this worksheetTwo products and one subtraction
For a matrix with rows (a, b) and (c, d), the determinant is the scalar ad − bc. Parentheses matter when the second product is negative.
Algebraic questions show one variable and a supplied value. Substitute that value into the entries first, then complete the numeric diagonal products and subtraction. A zero or negative result is valid.
Learning objective
What this activity builds
Substitute the supplied variable value when required, then use the difference of two diagonal products.
Worked example
Find the determinant of the 2 × 2 matrix whose rows are (3, −2) and (5, 4).
22.
Use ad − bc: 3·4 − (−2·5) = 12 − (−10) = 22.
Teaching notes
Make the practice count
- Name the four positions a, b, c and d before multiplying.
- Substitute the supplied value into every occurrence of the variable first.
- Keep parentheses around a negative diagonal product.
- Write the subtraction sign between the two complete products.
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