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.
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Basic matrix operations worksheets
Practice six matrix addition, subtraction and scalar multiplication questions with numeric, algebraic or mixed entries. Undefined cases make dimension checks part of the work.
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Check the dimensions first. For addition and subtraction, combine entries in matching positions. For scalar multiplication, multiply every entry by the scalar.
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Customize this worksheetPosition and dimensions come first
A sum or difference is defined only when both matrices have the same dimensions. Once that check passes, each output entry comes from the two entries in the same position. A scalar multiple keeps the matrix dimensions and changes every entry.
Choose numeric, algebraic or mixed entries. The dimension setting can keep every operation defined, focus on undefined operations or combine both cases.
Learning objective
What this activity builds
Apply an operation entry by entry after checking that the matrix dimensions make it valid.
Worked example
Add two 2 × 2 matrices. A has rows (2, x) and (−1, 3); B has rows (4, 2x) and (5, −3).
The sum has rows (6, 3x) and (4, 0).
Both matrices are 2 × 2, so the sum is defined. Add the entries that occupy the same row and column.
Teaching notes
Make the practice count
- Say the number of rows before the number of columns.
- Mark matching positions before combining entries.
- Distribute a scalar to every entry, including zero and negative entries.
- Ask for “undefined” when dimensions do not match instead of forcing an answer.
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