Search our library of Further Mathematics A Level questions

Top answers

Further Mathematics

A Level

Let A, B and C be nxn matrices such that A=BC-CB. Show that the trace of A (denoted Tr(A)) is 0, where the trace of an nxn matrix is defined as the sum of the entries along the leading diagonal.

This is the type of question which requires some out of the box thinking. A sketch is presented below: We start by defining A = (a_ij), B = (b_ij) and C = (c_i...

Answered by Daniel G. • Further Mathematics tutor

3204 Views

Express sin(5theta) in terms of sin(theta) and powers of sin(theta) only.

Consider the expression (cos(theta) + i*sin(theta))⁵. (Where theta a real parameter).By De Moirve's theorem, we know this expression is equivalent to cos(5theta) + i sin(5theta).We can also ap...

Answered by Peter F. • Further Mathematics tutor

4697 Views

A mass m=1kg, initially at rest and with x=10mm, is connected to a damper with stiffness k=24N/mm and damping constant c=0.2Ns/mm. Given that the differential equation of the system is given by d^2x/dt^2+(dx/dt *c/m)+kx/m=0, find the particular solution.

The system is described by a homogeneous, second order differential equation d²x/dt²+(dx/dt * c/m) + kx/m =0. First, substitute the known constants (m,k,c) to get d²x/dt<...

Answered by Christodoulos K. • Further Mathematics tutor

2460 Views

Find the eigenvalues and eigenvectors of the following 3x3 matrix (reading left to right, top to bottom): (1 0 2 3 1 1 2 0 1)

The eigenvalues are given by the characteristic equation (1-x)((1-x)^2-4)=0, which gives the values x=1, x=-1 and x=3 . These eigenvalues correspond to the eigenvectors (0, 1, 0), (1, -1, -1) and (1, -...

Answered by Joshua P. • Further Mathematics tutor

2018 Views