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A matrix M has eigenvectors (3,1,0) (2,8,2) (1,1,6) with corresponding eigenvalues 1, 6, 2 respectively. Write an invertible matrix P and diagonal matrix D such that M=PD(P^-1), hence calculate M^5.

Without even knowing M, the candidate can calculate M^5. This will follow from the fact that P is the matrix consisting of the eigenvectors of M as columns, and D will have the eigenvalues (in matching co...

CB
Answered by Cameron B. Maths tutor
2904 Views

A smooth 4g marble is held at rest on a smooth plane which is fixed at 30 degrees to a horizontal table. The marble is released from rest - what speed is the marble travelling at 5 seconds after being released? Let g = 9.8ms^2

This question involves forces and kinematics. First begin by drawing the situation and identifying the forces acting on the marble. The weight of the marble acts vertically downwards and is equal to the m...

MR
Answered by Maya R. Maths tutor
2835 Views

How do I write about context effectively?

Context, as an essential part of the A-level marking criteria, is an often overlooked element. It is not only important to remember that each piece of literature was created within and influenced by its o...

BA
3920 Views

To what extent was the practice of consensus politics undermined during the period of the Thatcher governments?

The election of Margaret Thatcher in 1979 is often viewed as the beginning of the end for the post-war consensus that had developed in Britain. The post-war period of 'consensus' was defined by a paternal...

NG
3134 Views

'The Great Depression caused the fall of the Weimar Republic'. Assess the validity of this view.

The collapse of the Weimar Republic has been an area of contentious debate for historians seeking to explain the emergence of the Nazi phenomenon. The political and socio-economic climate of 1930s’ German...

NG
Answered by Neha G. History tutor
6081 Views

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