Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Try to solve some simultaneous equations using matrix inverses.

Cofactors Determinant and inverse of a 3x3 matrix.

Matrix by scalar and matrix by matrix multiplication exercises.

Exercises on inverting 2x2 and 3x3 matrices.

Semi-worked example of inverting a 3x3 matrix using cofactor, adjoint and determinant.

Exercises on calculating the determinant of 2x2 and 3x3 matrices.

Exercises covering matrix addition and subtraction

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Find eigenvalues and eigenvectors of $A$ $2 \times 2$ matrix.

Given a generator matrix for a linear code, write a parity check matrix, compute the syndrome of a word, and decide if it's a codeword.

Addition and subtraction of matrices; multiplication by scalar.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Multiplication of $2 \times 2$ matrices.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Find the determinant of a $4 \times 4$ matrix.

Find the determinant of a $3 \times 3$ matrix.

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Ask the student to find a matrix corresponding to a given rotation about the origin.

Then ask them to find the determinant. Their answer is marked against the matrix they gave, not just the correct one.

Finally, ask them to find the inverse of their matrix. Marking is against the matrix and determinant they gave.

This question adds a CSS rule to hide the brackets around the matrix input.

Some custom CSS restyles the matrix input so it looks like a fraction, with input boxes on top and bottom.

Ideally, there should be a fraction input part type, or an option for the number entry part to display a fraction input.