Looking at gradients and values for x and y for straight-line graphs

Solving pair of simultaneous (linear) equations

Find a regression equation.

This exercise will help you rearrange a linear equation to find the value of a given variable

This exercise will help you rearrange a linear equation to find the value of a given variable

Factorising basic quadratics into linear expressions

Factorising further basic quadratics into linear expressions

Use a piecewise linear graph of speed against time to find the distance travelled by a car.

Finally, use the total distance travelled to find the average speed.

A 2D linear programming problem: optimise the profit from producing two different kinds of product, which both use the same limited resources.

A JSXGraph diagram illustrates the problem and can be used to find an answer.

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

No description given

No description given

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Set up so that sometimes it has infinitely many solutions (one free variable), sometimes unique solution. Scaffolded so meant for formative. The variable d determines the cases (d=1: unique solution, d-0: infinitely many solutions). The other variables are set up so that no entries become zero for some randomisations but not others.

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

To understand matrix multiplication in terms of linear combinations of column vectors.

No description given

No description given

No description given

This is a Numbas test covering linear programming techniques.

Linear combinations of $2 \times 2$ matrices. Three examples.

True/false question type to assess knowledge of the basics of linear correlation and regression.

Moving averages, regression and seasonal adjustments.

Conduct a linear regression analysis using a spreadsheet or stats program.

Find a matrix whose associated linear map maps the unit square to the shown parallelogram. Match figures "of linear maps" with matrices.

Compute how many linear maps $\mathbb F_p^n\to \mathbb F_p^m$ exist which take prescribed values on a given set of elements in $\mathbb F_p^n$ (which is linearly dependent).