Question

Problem 1 (Linear Systems of Equations). (a) Determine the values of a for which the follow- ing system of equations have no solution, exactly one solution, infinitely many solutions (a + 2)y + (a2-4)2 = (0-2) (b) If A = 4-1 0 a 2b a a be the augmented matrix of a linear system of equations then evaluate the values of a and b for which the linear system has no solution? exactly one solution? one parameter solution? two parameter solution? c) Explain how would you adopt the method of solving linear systems of equations to find a solution X such that AXB = C, where A a m x n matrix, B a p x q matrix and C a m x q are given Describe all the cases: the case for unique solution, no solution and infinitely many solutions Hint: A single system Ax = c provides a solution x E Rn for each c E Rm. Think of the columns of C 1 23 n-1 0 1 2 n-2 n-1 0 01 n-3 n-2 d) Let for each n1: A 0 0 0 1 Show that each An is invertible Hint: Use matrix representation. Mark Distribution for Problem 1: 551010 30 marks] c) Explain how would you adopt the method of solving linear systems of equations to find a solution X such that AXB-C, where A a m × n matrix, B ap × q matrix and C a m × q are given y many solutions Hint: A single system Ax columns of C c provides a solution x E Rn for each c E Rm. Think of the

Answer 1

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