Top answers

How can you divide an algebraic expression by another algebraic expression?

I would begin the session with checking a basic understanding of the methods of long division, as these will not have been taught very recently. Many students will have been using short division, as it is qu...
JH
3555 Views

Show that (n^2) + (n+1)^2 + (n+2)^2 = 3n^2 + 6n + 5, Hence show that the sum of 3 consecutive square numbers is always 2 away from a multiple of 3.

Expanding out the Brackets: (n 2 )+ (n 2 + n + n + 1) + (n 2 + 2n + 2n +4) = (n 2 ) + (n 2 +2n+1) + (n 2 +4n+4) =3n 2 + 6n +5 Using this result: Three consecutice numbers: n, n+1, n+2 So three consecutive sq...
JC
3693 Views

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 determinant of the (n - 1) (n - 1) matr...
ET
3668 Views

Can you explain induction and go through an example?

Induction is a method that can be used to prove that a mathematical statement holds for possitive integers, n. It usually consists of four steps, as follows: 1) Basis: Show that the statement to be proved ho...
AS
3324 Views

Find the solution of 3^{4x} = 9^{(x-1)/2}.

First, recognise that 3^2 = 9. Recall the rule for multiplying indices, that (a^b)^c = a^{bc}. Then, substitute 3^2 in place of 9 to get 3^{4x} = (3^2)^{(x-1)/2}. Use the rule for multiplying indices, so tha...
CO
2599 Views