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.
Preview and downloadCheck the structure. Then calculate.
Matrix worksheets
Add, subtract, scale and multiply matrices, then evaluate 2 × 2 and 3 × 3 determinants as exact scalar expressions.
Choose a practice sheetBuild the next skill
Build the entry-by-entry foundation
Begin with sums, differences and scalar multiples before changing the shape of a result.
Build the next skill
Use rows and columns
Practice matrix products, then alternate between product questions and the basic matrix operations.
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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Matrices
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.
Preview and downloadOne scalar from a square matrix
Evaluate determinants
Use ad − bc for a 2 × 2 matrix, then extend the same minor calculation through a signed first-row cofactor expansion for a 3 × 3 matrix. Algebraic questions provide one variable value to substitute before the numeric determinant calculation.
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.
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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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Find 2 × 2 matrix inverses
Use ad − bc to decide whether an inverse exists. When the determinant is nonzero, swap the diagonal entries, negate the off-diagonal entries and divide by the determinant, keeping fractional entries exact.
Matrices
Matrix inverse worksheets
Decide whether six numeric 2 × 2 matrices have inverses, then find six exact inverses or state that no inverse exists.
Preview and downloadPreserve the multiplication order
Solve exact matrix equations
Isolate a signed scalar multiple in A + cX = B, or solve AX = B by multiplying by A⁻¹ on the left. Six-question worksheets use exact results and separate worked keys.
Matrices
Matrix equations worksheets
Solve six exact matrix equations by isolating a scalar multiple of X or multiplying by a 2 × 2 inverse on the left.
Preview and downloadDeterminants applied to systems
Solve with Cramer's rule
Use column-replacement determinants to solve 2 × 2 and 3 × 3 systems. A nonzero coefficient determinant gives exact determinant quotients; a zero determinant requires augmented-matrix rank evidence to distinguish infinitely many solutions from no solution.
Matrices
Cramer's rule 2 × 2 worksheets
Solve twelve two-variable systems with Cramer's rule. Practice unique, infinitely many and no-solution systems with exact determinant reasoning.
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Matrices
Cramer's rule 3 × 3 worksheets
Solve twelve three-variable systems with Cramer's rule. Use exact determinants and rank evidence for unique, infinitely many and no-solution systems.
Preview and downloadChoose a starting point
Open the generator with a focused combination of entry types and dimension cases.
Start with defined numeric operations
Focus on matching positions and scalar distribution with compatible dimensions.
Open this setup →Combine algebraic entries
Simplify exact polynomial entries while deciding whether each operation is defined.
Open this setup →Practice compatible products
Use numeric entries to establish the row-by-column procedure.
Open this setup →Check products before calculating
Mix entry types and include products whose inner dimensions do not match.
Open this setup →Switch between matrix methods
Use exact algebraic entries while alternating between basic operations and matrix products.
Open this setup →Questions that reveal the method
- What are the dimensions of each matrix?
- Which dimensions must match for this operation?
- Which row and column produce this product entry?
- Which cofactor sign applies to this determinant term?