Matrices
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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Mixed matrix operations worksheets
Work through six questions that mix addition, subtraction or scalar multiplication with separate matrix products. Exact entries and dimension-aware answers distinguish valid expressions from undefined ones.
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Read the operation before checking dimensions. Match the full dimensions for a sum or difference; match the inner dimensions for a product.
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Customize this worksheetChoose the dimension rule from the operation
Addition and subtraction require two equal shapes. Matrix multiplication instead compares the columns of the left factor with the rows of the right factor. Naming the operation first prevents one dimension rule from being applied to every question.
Each mixed sheet has three basic-operation questions and three separate matrix products. Exact polynomial entries keep the algebra visible in both kinds of work.
Learning objective
What this activity builds
Choose the correct dimension rule and calculation method for each matrix operation in a mixed set.
Worked example
A and B are 2 × 2. C is 2 × 3 and D is 3 × 1. Are A + B and CD defined?
Both are defined.
A and B have equal dimensions, so they can be added. The inner dimensions of CD are both 3, so their product is also defined and has dimensions 2 × 1.
Teaching notes
Make the practice count
- Name the operation before applying a dimension rule.
- For a sum or difference, compare both dimensions.
- For a product, compare the inner dimensions and predict the outer dimensions.
- Use the mixed set to notice when a learner applies one rule to every operation.
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