Matrices
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.
Preview and downloadMatrices practice
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.
Ready-made English PDF · fixed settings
Customization below makes a separate PDF.
Fixed English ready-made files. Custom settings below apply only to the configured PDF.
Ready to print
Start with a ready-made worksheet
On an algebraic question, substitute the given value into the matrix first. Then expand across the first row with signs positive, negative, positive and combine the numeric cofactor terms exactly.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetKeep the cofactor signs visible
A first-row expansion uses the alternating sign pattern positive, negative, positive. Each first-row entry multiplies the 2 × 2 determinant left after its row and column are removed.
For an algebraic question, substitute the supplied value first. The key then shows the signed numeric cofactor calculation and exact numeric determinant.
Learning objective
What this activity builds
Substitute the supplied variable value when required, then use a signed first-row cofactor expansion.
Worked example
Find the determinant of the matrix with rows (1, 2, 0), (3, −1, 4) and (2, 5, 1).
−11.
First-row expansion gives 1[(−1)(1) − 4(5)] − 2[3(1) − 4(2)] + 0[3(5) − (−1)(2)] = −21 + 10 = −11.
Teaching notes
Make the practice count
- Substitute the supplied value into every occurrence of the variable first.
- Write the first-row sign pattern +, −, + above the matrix.
- Cover one row and one column to identify each minor.
- Evaluate each 2 × 2 determinant before applying its cofactor sign.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose the entry type, update the preview and print the same determinant questions with a separate answer key.
Enlarged pages scroll. PDF size stays the same.
A useful next step
Related activities
Matrices
Matrix multiplication worksheets
Complete six matrix products with exact numeric, algebraic or mixed entries, and identify products that are undefined because the inner dimensions differ.
Preview and download
Polynomials
Adding and subtracting polynomials worksheets
Print a 10-question adding and subtracting polynomials worksheet. Choose two or three grouped polynomials with four to nine terms and worked answers.
Preview and download