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Maths 2 week 2 important questions

Week 2 of Mathematics for Data Science II: Cramer's rule, echelon form, Gaussian elimination. Extra important questions based on the recent, changing patterns of the exams, from basic to advanced. Practise them in learning mode: each question has a worked solution.

Question 1

Numerical answer

For the system

3x+2y=8−x−3y=−12\begin{aligned} 3x + 2y &= 8 \\ -x - 3y &= -12 \end{aligned}

solved by Cramer's rule, find the determinant DD of the coefficient matrix.

Question 2

One correct option

For the system

−x+y−z=−83x+4y−2z=−123x+3y−3z=−12\begin{aligned} -x + y - z &= -8 \\ 3x + 4y - 2z &= -12 \\ 3x + 3y - 3z &= -12 \end{aligned}

solved by Cramer's rule, find DzD_z (the determinant obtained by replacing the column of z with the right-hand side).

  1. A

    3535

  2. B

    3737

  3. C

    7272

  4. D

    3636

Question 3

Numerical answer

Use Cramer's rule to find yy in the system

−2x+4y=−144x+y=10\begin{aligned} -2x + 4y &= -14 \\ 4x + y &= 10 \end{aligned}

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