MAT1503 Oct/Nov 2014 exam paper — questions

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  1. Question 1(a)(i) · Matrices and systems of equations · 1 mark

    All parts refer to Question 1 of the MAT1503 October/November 2014 Linear Algebra paper. Consider the system of equations given by x1 - 3x2 = 2 and 2x2 = 6. Write down the coefficient matrix corresponding to this system.Show the full question

  2. Question 1(a)(ii) · Matrices and systems of equations · 3 marks

    All parts refer to Question 1 of the MAT1503 October/November 2014 Linear Algebra paper. Using the same system of equations, x1 - 3x2 = 2 and 2x2 = 6, apply back substitution to solve for x1 and x2.Show the full question

  3. Question 1(b)(i) · Matrices and systems of equations · 5 marks

    All parts refer to Question 1 of the MAT1503 October/November 2014 Linear Algebra paper. Let A, B and C be the matrices A = [[1,2],[3,4]], B = [[2,1],[-3,2]] and C = [[1,0],[2,1]]. Determine whether or not A(BC) = (AB)C by computing both sides.Show the full question

  4. Question 1(b)(ii) · Matrices and systems of equations · 5 marks

    All parts refer to Question 1 of the MAT1503 October/November 2014 Linear Algebra paper. Using the same matrices A = [[1,2],[3,4]], B = [[2,1],[-3,2]] and C = [[1,0],[2,1]], determine whether or not A(B + C) = AB + AC by computing both sides.Show the full question

  5. Question 1(c) · Matrices and systems of equations · 5 marks

    All parts refer to Question 1 of the MAT1503 October/November 2014 Linear Algebra paper. Let D and E be nonsingular matrices. Show that (DE)^-1 = E^-1 D^-1.Show the full question

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