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.

A randomly generated list of numbers is shown to the student. They must tick every occurrence of the lowest number. The number of occurrences isn't always the same - sometimes the minimum is unique and sometimes it is repeated. The map function makes it easy to construct a marking matrix.

The student has to compute $a^b$ and $b^a$, then decide which of the two is bigger.

This question shows how to set up a custom marking matrix for the "choose one from a list" part, based on values used elsewhere in the question. It could use adaptive marking to use the student's incorrect values for the comparison, but doesn't at the moment.

Write down a lexicographic parity check matrix for a Hamming code and correct two received codewords.

Write down the lexicographic parity check matrix for a Hamming code, and correct two received codewords.

Given a matrix in the field $\mathbb{Z}_n$. By reducing it to row-echelon form (or otherwise), find a basis for the row space of the matrix, as a list of vectors.

Given a set of codewords generating a code, write down a generator matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Compute the minimum distance between codewords of a code, given a parity check matrix.