MAT1503 May/Jun 2012 exam paper — questions

🔒 Scan locked

  1. Question 1.1 · Matrices and systems of equations · 5 marks

    Given the matrices A = [[-1, 0], [2, 3]] and B = [[1, 2], [3, 0]], determine whether or not AB = BA.Show the full question

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

    Reduce the following matrix to reduced row-echelon form: the 3x3 matrix with rows [0, 3, 9], [0, 2, -4], and [0, 0, 3].Show the full question

  3. Question 1.3 · Matrices and systems of equations · 8 marks

    Solve the following system of equations: 3x + 4y + z = 1; 2x + 3y = 0; 4x + 3y - z = -2.Show the full question

  4. Question 1.4 · Matrices and systems of equations · 7 marks

    Let A be the matrix [[2, 1], [-1, 0]]. Using row operations, find A inverse, and verify this by showing that A times A inverse equals A inverse times A equals I2, where I2 denotes the 2x2 identity matrix.Show the full question

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

    Consider the 3x3 matrix A whose rows are 4, -1, 5 in the first row; 6, 2, 1 in the second row; and 0, 2, 1 in the third row. Write down this matrix A and calculate its determinant.Show the full question

The full Spot Map and the marks by year — and this paper’s scan.