Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Multiplication of $2 \times 2$ matrices.

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Multiplication of $2 \times 2$ matrices.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

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 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.

Find the determinant of  a random (3x3) matrix.

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

The CSS preamble adds a vertical line down the input for part b, to separate the two parts of the matrix.

This question tests students knowledge of basic matrix arithmetic.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

Calculate the magnitude of a 2-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v1\\v2}$.

(a) Read subscript notation to identify an element in a 3x3 matrix; (b) chose the correct subscripted name from a list for a given element in a 3x3 matrix.

Find the determinant of a random (2x2) matrix.

Find principal stresses by finding the eigenvalues of the matrix

Matrixausfüllen

Cofactors Determinant and inverse of a 3x3 matrix.

Cofactors Determinant and inverse of a 3x3 matrix.

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

Alternative version of Graphs: Match graph to its adjacency matrix, where the student must match an adjacency matrix to a graph.

The student is shown one graph, and asked to type the adjacency matrix

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

The student is asked to enter a given matrix, but they're only required to fill in the upper triangle.

A custom marking algorithm fills in any empty cells in the lower triangle of the student's answer with the corresponding cell in the upper triangle.

The student is still warned if they leave any cells empty in the upper triangle.

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

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

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