MAT1503 May/Jun 2013 exam paper — questions

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  1. Question 1.1 · Matrices and systems of equations · 3 marks

    Give a description of the elementary row operations that can be performed on a matrix.Show the full question

  2. Question 1.2 · Matrices and systems of equations · 4 marks

    Show, by substitution, that x = 19t - 35, y = 25 - 13t and z = t satisfy both equations of the system 2x + 3y + z = 5 and 5x + 7y - 4z = 0, thereby verifying that this is a solution of the system.Show the full question

  3. Question 1.3(a) · Matrices and systems of equations · 2 marks

    Evaluate the matrix expression formed by subtracting 5 times the matrix [[3,0,-2],[1,-1,2]] from the matrix [[3,2,1],[5,1,0]].Show the full question

  4. Question 1.3(b) · Matrices and systems of equations · 3 marks

    Given the matrix equation 2A - B = 5(A + 2B), express the matrix A in terms of the matrix B.Show the full question

  5. Question 1.4(a) · Matrices and systems of equations · 5 marks

    Let A be the matrix [[3,-1],[0,-2]] and let I2 be the 2x2 identity matrix [[1,0],[0,1]]. Compute the matrix expression A^2 - A - 6I2.Show the full question

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