Top answers

The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.

a) We know that, for a general quadratic equation that can be written as : a x 2 +bx+c=0, the sum of its roots (S) is equal to -b/a and the product of its roots (P) is equal to c/a (which can easily be verif...
BC
26735 Views

A useful practice: how to determine the number of solutions of a system of linear equations beforehand

We have a system of n linear equations incorporated by A x = b , with A being a n x p matrix of numeric coefficients, x being a p-dimensional column vector of variables and b being a numeric n-dimensional co...
FB
4194 Views

Find the determinant of a 3x3 matrix.

Will need a whiteboard so I can draw a matrix to fully explain.
SM
3207 Views

What is the modulus of 3+4i?

5
VC
3246 Views

Find the eigenvalues and corresponding eigenvectors of the following matrix: A = [[6, -3], [4, -1]]. Hence represent the matrix in diagonal form.

The first eigenvalue is 3, whose corresponding eigenvector is (1, 1), and the second eigenvalue is 2, whose corresponding eigenvector is (3, 4). In diagonal form, A = PDP^-1, where P = [[1, 3], [1, 4]] and D...
MU
3742 Views