How often Matrices and systems of equations is asked

Where it was asked

• May/Jun 201225 marks
• Oct/Nov 201126 marks
• May/Jun 201114 marks

The questions

1. May/Jun 2012, Q1.15 marks

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

2. May/Jun 2012, Q1.25 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].

3. May/Jun 2012, Q1.38 marks

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

4. May/Jun 2012, Q1.47 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.

5. Oct/Nov 2011, Q1.14 marks

   Consider the following system of linear equations: 2x + y - 3z = 2; 2x - 3y + z = 10; -2x + y + z = -6. For the system of linear equations 2x + y - 3z = 2, 2x - 3y + z = 10, -2x + y + z = -6, determine whether there exists a value of a such that the triple (a, 1, 3) satisfies all three equations simultaneously. If such a value exists, state what a equals; if no such value exists, give a clear explanation for why not.