Show that the matrix A is non-singular for all real values of a
Given: A = [a -5; 2 a+4]. 1) First find the determinant of A using the known formula => det A = a2+ 4a + 10. A singular matrix is one in which it's determinant equals zero (the determinant of a matrix is a number that captures information about the characteristics of the matrix). The roots of the quadratic are complex, so the graph never equals zero/ no real roots. Therefore it must be a non-singular matrix.
Related Further Mathematics A Level answers
All answers ▸Use de Moivre’s theorem to show that, (sin(x))^5 = A sin(5x) + Bsin(3x) + Csin(x), where A , B and C are constants to be found.
Find the reflection of point P(2,4,-6) in the plane x-2y+z=6
A rectangular hyperbola has parametric equations x = 4t, y = 4/t , (z non 0). Points P and Q on this hyperbola have parameters t = 1/4 and t = 2. Find the equation of the line l which passes through the origin and is perpendicular to the line PQ.
Prove, by induction, that 4^(n+1) + 5^(2n-1) is always divisible by 21