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Prove that (AB)^-1 = B^-1 A^-1

This problem can be solved in 8 steps:

1. Let AB = C

2. A^-1AB = A^-1C

3. IB = A^-1C as the identity matrix I = A^-1A

Answered by Katie H. • Further Mathematics tutor

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Differentiate artanh(x) with respect to x

First we set y=artanh(x). Then we rearrange such that tanh(y)=x. There several approaches to find dy/dx, but the quickest is to use implicit differentiation.

The differential of tanh(y) is sech

Answered by Sam H. • Further Mathematics tutor

10197 Views

Solve x^3=1 giving all the roots between -pi<=theta<=pi in exponential form

x^3=1=e^2(pi)ik

x=e^2(pi)ik/3

The three roots are

k=0 x=1

k=1 x=e^2(pi)*i/3

k=-1 x=e^-2(pi)ik/3

Answered by Anmol A. • Further Mathematics tutor

2299 Views

A golf ball is hit from horizontal ground with speed 10 m/s at an angle of p degrees above the horizontal. The greatest height the golf ball reached above ground level is 1.22m. Model the golf ball as a particle and ignore air resistance. Find p.

Initial horizontal speed of particle = 10cos(p) m/s. Initial vertical speed of particle = 10sin(p) m/s. ('U' in suvat.) There are no forces other than gravity acting on the particle so the vertical accele...

Answered by Sachin R. • Further Mathematics tutor

4187 Views

Can you show me how to solve first order differential equations using the integrating factor method?

To use the integrating factor method your first order DE must be of the form dy/dx + f(x)y =g(x), where f(x) and g(x) are any functions that depend only on x. lets say f(x)=3x^2 and g(x)=2, (If I feel the...

Answered by Ryan A. • Further Mathematics tutor

2771 Views