MAT1503 May/Jun 2014 exam paper — questions

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  1. Question 1.1 · Matrices and systems of equations · 1 mark

    Consider the system of linear equations consisting of x + 2y = 0 and y = 1. Write down the augmented matrix that represents this system.Show the full question

  2. Question 1.2 · Matrices and systems of equations · 2 marks

    Using the same system of linear equations, namely x + 2y = 0 and y = 1, solve for the value of x.Show the full question

  3. Question 1.3 · Matrices and systems of equations · 3 marks

    Reduce the matrix with rows (1, 1, -1, 4), (2, 1, 3, 0) and (0, 1, -5, 8) to row-echelon form.Show the full question

  4. Question 1.4 · Matrices and systems of equations · 6 marks

    Let A be the 3x3 matrix with rows (1, -2, 2), (2, 1, 1) and (1, 0, 1). Let B be the matrix with rows (1, 2, -4), (-1, -1, 3) and (-1, -2, 5). Show that B is equal to the inverse of A, that is B = A^{-1}. As a hint, compute the products AB and BA to confirm this.Show the full question

  5. Question 1.5 · Matrices and systems of equations · 5 marks

    Consider the system of linear equations: x1 - 2x2 + 2x3 = 3; 2x1 + x2 + x3 = 0; x1 + x3 = -2. Let X be the column vector (x1, x2, x3) and let Y be the column vector (3, 0, -2). Observe that this system can be written in matrix form as AX = Y, where A is the same matrix given in part 1.4 above (rows (1,-2,2), (2,1,1), (1,0,1)). Using the inverse A^{-1} found in part 1.4 (the hint being to use A^{-1} given there), solve the system for X.Show the full question

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