A-LevelFurther MathematicsParametric EquationsMay/June 2016Paper 1 Q1114 Marks
ANSWER ONLY ONE OF THE FOLLOWING TWO ALTERNATIVES. OR The linear transformation T : R⁴ → R⁴ is represented by the matrix M, where M = [[1,-2,3,-4],[2,-4,7,-9],[4,-8,14,-18],[5,-10,17,-22]] Find the rank of M. Obtain a basis for the null space K of T. Evaluate M [[1],[-2],[2],[-1]] and hence show that any solution of Mx = [[15],[33],[66],[81]] has the form [[1],[-2],[2],[-1]] + λe₁ + μe₂, where λ and μ are scalars and {e₁, e₂} is a basis for K. Hence obtain a solution x' of (*) such that the sum of the components of x' is 6 and the sum of the squares of the components of x' is 26.
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