MAT1503 May/Jun 2017 exam paper — questions

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  1. Question 1.1 · Matrices and systems of equations · 4 marks

    State and explain the defining properties that a matrix must satisfy in order to be in reduced row-echelon form.Show the full question

  2. Question 1.2 · Matrices and systems of equations · 6 marks

    Use Gauss elimination to solve the following system of three equations in x, y and z: x - 2y + 3z = 9; -x + 3y = -4; 2x - 5y + 5z = 17.Show the full question

  3. Question 1.3 · Matrices and systems of equations · 5 marks

    Given the 2x2 matrix A, whose first row is 2, 0 and whose second row is 0, 3, compute the matrix power A cubed (A^3).Show the full question

  4. Question 1.4 · Matrices and systems of equations · 10 marks

    Given the 3x3 matrix B whose rows are (1, -1, 0), (1, 0, -1) and (-6, 2, 3), use row operations to compute the inverse matrix B^-1, and then verify that B times B^-1 equals B^-1 times B equals the 3x3 identity matrix I3.Show the full question

  5. Question 2.1 · Determinants and Cramer's rule · 5 marks

    Given the matrix A = [[3, 2, -1], [1, 6, 3], [2, -4, 0]], determine adj(A), the adjoint (adjugate) of A.Show the full question

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