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 ▸Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.
Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).
Solve x^2+8x-5=0 using completing the square
Understanding differentiation from first principle.