Grade 12 - Matrices
Explanation and Free Practice Resources
Construct and interpret matrices from data, identify their dimensions, rows, columns, and elements, test matrix equality and multiplication compatibility, and perform addition, subtraction, scalar multiplication, and transposition using their properties. Multiply matrices and vectors, determine product dimensions, apply multiplication properties and the identity matrix, and use matrices to model, combine, and interpret transformations and systems of linear equations. Calculate 2-by-2 and 3-by-3 determinants using minors and cofactors, determine invertibility, find and verify inverses using the adjugate, and solve matrix equations and linear systems with inverse matrices.
On this page:
- Master skills like “Add matrices”, “Subtract matrices”, and “Multiply two matrices” with unlimited, free practice problems
- Download (or modify) free worksheets on Matrices you can use at home or in class with practice problems across all skills in this group including “Construct the cofactor matrix”, “Multiply a matrix by a scalar”, “Construct the matrix of minors”.
Matrices: Individual Skills
Master 35 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Add matrices
- Apply a transformation matrix to coordinate points
- Apply properties of matrix transposes
- Calculate cofactors of a matrix
- Calculate minors of a 3 by 3 matrix
- Calculate the determinant of a 2 by 2 matrix
- Calculate the determinant of a 3 by 3 matrix using cofactor expansion
- Calculate the dot product of a matrix row and column
- Calculate the inverse of a 2 by 2 matrix
- Calculate the inverse of a 3 by 3 matrix using cofactors
- Construct the cofactor matrix
- Construct the matrix of minors
- Determine the adjugate of a matrix
- Determine the dimensions of a matrix
- Determine the dimensions of a matrix product
- Determine the sign of a cofactor from its position
- Determine the transpose of a matrix
- Determine whether two matrices can be multiplied
- Expand a determinant along a specified column
- Expand a determinant along a specified row
- Identify a matrix element from its row and column indices
- Identify row, column, square, zero, and identity matrices
- Identify rows and columns of a matrix
- Identify the minor associated with a matrix element
- Interpret a matrix product in context
- Interpret data represented by a matrix
- Interpret matrix notation for individual elements
- Interpret the determinant as a test of invertibility
- Multiply a matrix by a column vector
- Multiply a matrix by a scalar
- Multiply a row matrix by a column matrix
- Multiply two matrices
- Select an efficient row or column for cofactor expansion
- Simplify expressions involving matrix addition, subtraction, and scalar multiplication
- Subtract matrices
Practice 'Add matrices'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
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Download/Modify Free Grade 12 'Matrices' Worksheet
Print this free 'Matrices' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Add matrices
- Apply a transformation matrix to coordinate points
- Apply properties of matrix transposes
- Calculate cofactors of a matrix
- Calculate minors of a 3 by 3 matrix
- Calculate the determinant of a 2 by 2 matrix
- Calculate the determinant of a 3 by 3 matrix using cofactor expansion
- Calculate the dot product of a matrix row and column
Explore More Grade 12 Math
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- Derivatives
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- Financial Mathematics
- Function Characteristics
- Function Transformations and Compositions
- Lines and Planes
- Polynomial and Rational Functions
- Probability Distributions
- Rates of Change and Limits
- Statistical Analysis