MAT1503 May/Jun 2016 exam paper — questions

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  1. Question 1.1.1 · Matrices and systems of equations · 3 marks

    Demonstrate that the values x = 2 and y = -1 satisfy the pair of equations 2x - y = 5 and x + 2y = 0 simultaneously.Show the full question

  2. Question 1.1.2 · Matrices and systems of equations · 3 marks

    Give a complete explanation of whether the system consisting of x + y = 1 and 2x + 2y = 3 has a solution or not.Show the full question

  3. Question 1.2 · Matrices and systems of equations · 5 marks

    Determine the reduced row echelon form of the matrix A, where A has rows (1, 2, 1, 4), (3, 8, 7, 20) and (2, 7, 9, 23).Show the full question

  4. Question 1.3.1 · Matrices and systems of equations · 6 marks

    Given the general 2x2 matrix B with entries a, b in the first row and c, d in the second row, prove that B squared equals (a + d)B minus (ad - bc)I, where I denotes the 2x2 identity matrix.Show the full question

  5. Question 1.3.2 · Matrices and systems of equations · 8 marks

    Using the result from 1.3.1, namely that B^2 = (a + d)B - (ad - bc)I, it follows that B^3 = (a + d)B^2 - (ad - bc)B and B^4 = (a + d)B^3 - (ad - bc)B^2. Apply these formulae to compute C^2, C^3 and C^4 for the matrix C whose rows are (2, 1) and (1, 2).Show the full question

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