MAT1503 Oct/Nov 2015 exam paper — questions

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

    Given the matrix equation x1 multiplied by the column vector (2, 5), plus x2 multiplied by the column vector (3, -4), plus x3 multiplied by the column vector (-2, 2), equals the column vector (5, 6), rewrite this matrix equation as an equivalent system of linear equations. Thereafter, demonstrate that the values x1 = 2, x2 = 3 and x3 = 4 satisfy both the original matrix equation and the system of linear equations you obtained from it.Show the full question

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

    Determine two 1 x 3 matrices, X and Y, which simultaneously satisfy the following pair of matrix equations: X plus 2Y equals the row matrix [1 3 -2], and X plus Y equals the row matrix [2 0 1].Show the full question

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

    Given the 2 x 2 matrices A = [[3,1],[5,2]] and B = [[1,2],[3,4]], calculate the inverse matrix A^-1.Show the full question

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

    Using the inverse A^-1 that you calculated for A = [[3,1],[5,2]] in the previous part, determine a 2 x 2 matrix L that satisfies the equation A·L = B, where B = [[1,2],[3,4]].Show the full question

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

    Using the same inverse A^-1 computed earlier for A = [[3,1],[5,2]], determine a 2 x 2 matrix M that satisfies the equation M·A = B, where B = [[1,2],[3,4]].Show the full question

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