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Further Mathematics
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Consider the Matrix M (below). Find the determiannt of the matrix M by using; (a) cofactor expansion along the first row, (b) cofactor expansion along the second column

Matrix M is

-2 1 -4

1 -1  5

3  0  2

Let A be a square nxn matrix. Then, for each entry Aij (where 1 </= i < n, 1 </= j < n), the minor of Aij is A(^i;^j), the deter...

Answered by Evi T. Further Mathematics tutor
2735 Views

When using the method of partial fractions how do you choose what type of numerator to use and how do you know how many partial fractions there are?

There are as many fractions as there are factors of the denomenator.  If the denomenator of one of the partial fractions is linear then the numerator is a constant. If the denomenator is a linear term squ...

Answered by Charlie M. Further Mathematics tutor
2325 Views

When and how do I use proof by induction?

If you have a claim which says something about every element in a list of elements with each element depending on previous elements, induction might be a useful starting point. In your exams, that "l...

Answered by Steven R. Further Mathematics tutor
2680 Views

Using the substitution u = ln(x), find the general solution of the differential equation y = x^2*(d^2(y)/dx^2) + x(dy/dx) + y = 0

dy/dx = (dy/du)(1/x), d^2(y)/dx^2 = (d^2(y)/du^2)(1/(x^2)) - (dy/du)*(1/(x^2))   

(x^2)( (d^2(y)/du^2)(1/(x^2)) - (dy/du)(1/(x^2)) ) + x(dy/du)*(1/x) + y = 0       

<...
Answered by Isis K. Further Mathematics tutor
3876 Views

How do I express complex numbers in the form reiθ?

How do I express complex numbers in the form re? Complex numbers have a general form of a+ib, i being imaginary. To answer this it is best shown on an argand diagram. Plot your complex number...

Answered by Kishen L. Further Mathematics tutor
42637 Views

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