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.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Very elementary matrix multiplication. 

Questions on matrix arithmetic.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.

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

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$.

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Cofactors Determinant and inverse of a 3x3 matrix.

Multiplication of  matrices of different sizes.

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Cofactors Determinant and inverse of a 3x3 matrix.

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

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

Multiplication of $2 \times 2$ matrices.

Cofactors Determinant and inverse of a 3x3 matrix.

Multiplication of $2 \times 2$ matrices.

Elementary Exercises in multiplying matrices.