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Further Mathematics
A Level

How do I find the vector/cross product of two three-dimensional vectors?

Finding the cross product of two 3D vectors uses a very similar method to that of finding the determinant of a 3x3 matrix.

So, to find the cross product, just follow these simple steps:

    Answered by Luke M. Further Mathematics tutor
    5101 Views

Find the general solution for the determinant of a 3x3 martix. When does the inverse of this matrix not exist?

Let M be a 3x3 matrix s.t. M= |a b c| |g h i| |d e f|

Then Det(M)= a(Det(e,f,h,i))-b(Det(d,f,g,i))+c(Det(d,e,g,h).

Given that the determinant of a 2x2 matrix such as (e,f,h,i) is = ei-fh. Th...

Answered by Oskar D. Further Mathematics tutor
4114 Views

Find the general solution to the second order differential equation x'' - 2x' + x = e^(2t).

Firstly, note that the question only asks for the general solution (G.S.) to the equation, not for the whole solution. Now we have established what we need to find, construct the auxiliary equation. For t...

Answered by Amy B. Further Mathematics tutor
3946 Views

Find the modulus-argument form of the complex number z=(5√ 3 - 5i)

The easiest way to complete questions of these types is to first sketch an Argand diagram. With 5√ 3 on the x (real) axis and -5 on the y (imaginary) axis, the modulus would be calculated simply by using ...

Answered by Chris P. Further Mathematics tutor
23391 Views

Can you express 3 + 4j in polar form?

First, let's imagine the point 3 + 4j as a point on an Argand diagram, with coordinates 3,4. The polar form of an imaginary number is in the form re^(jθ), where r is the modulus of the number (the distanc...

Answered by Walter T. Further Mathematics tutor
14476 Views

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