Mathematics for Data Science II, Week-wise practice

Undated, Set week-02

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Question 1

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For the system

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

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

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For the system $$\begin{aligned} 3x + 2y &= 8 \\ -x - 3y &= -12 \end{aligned}$$ solved by Cramer's rule, find the determinant $D$ of the coefficient matrix. For the system $$\begin{aligned} -x + y - z &= -8 \\ 3x + 4y - 2z &= -12 \\ 3x + 3y - 3z &= -12 \end{aligned}$$ solved by Cramer's rule, find $D_z$ (the determinant obtained by replacing the column of z with the right-hand side). Use Cramer's rule to find $y$ in the system $$\begin{aligned} -2x + 4y &= -14 \\ 4x + y &= 10 \end{aligned}$$