MAT1503 Oct/Nov 2012 exam paper — questions

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

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

  2. Question 1(b) · Matrices and systems of equations · 6 marks

    Apply the Gauss-Jordan elimination method to solve the following system of three equations in two unknowns: 4x1 - 8x2 = 12; 3x1 - 6x2 = 9; -2x1 + 4x2 = -6.Show the full question

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

    Given the 2x2 matrix A with first row entries 0 and -1, and second row entries 1 and -1, compute the matrix A raised to the power 3 (that is, find A^3).Show the full question

  4. Question 1(d) · Matrices and systems of equations · 10 marks

    Consider the 3x3 matrix B whose rows are (2, 7, 1), (1, 4, -1) and (1, 3, 0). Using elementary row operations, determine the inverse matrix B^-1, and then confirm your result by showing that both B·B^-1 and B^-1·B equal the 3x3 identity matrix I3.Show the full question

  5. Question 2(a) · Determinants and Cramer's rule · 5 marks

    Given the matrix A with rows (3, 2, -1), (1, 6, 3) and (2, -4, 0), determine adj(A), the adjoint of A.Show the full question

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