MAT1503 Oct/Nov 2013 exam paper — questions

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

    Determine the solution set of the linear equation 7x − 5y = 3.Show the full question

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

    Reduce the matrix with first row 1, 3 and second row 2, 7 to row-echelon form.Show the full question

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

    Given that A is an m × n matrix and that the product A(BA) is defined, prove that B must be an n × m matrix.Show the full question

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

    Demonstrate that the matrix with rows (3, 5) and (1, 2) and the matrix with rows (2, −5) and (−1, 3) are inverses of one another.Show the full question

  5. Question 1(d)(i) · Matrices and systems of equations · 4 marks

    Let A be the 2×3 matrix with rows (1, 3, 2) and (1, 2, 2), and let B be the 3×2 matrix with rows (0, 3), (1, −1) and (−1, 0). Determine, with full explanation, whether the products AB and BA are defined.Show the full question

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