Three questions on linear combinations and products of matrices.

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2 questions. First question divides a cubic by a linear polynomial. The second divides a degree 4 polynomial by a degree 2 polynomial.

Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

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Straightforward solving linear equations question

Straightforward solving linear equations question.

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Shows how to define variables to stop degenerate examples.

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

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

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

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

Basic solving of linear equations

Solving linear equations

Shows how to define variables to stop degenerate examples.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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Identify parts of a statistical formula from a linear regression model

Factorising basic quadratics into linear expressions

Factorising further basic quadratics into linear expressions

Factorising further quadratics into linear expressions

Factorising further quadratics into linear expressions using the formula