2000019001 | math4u.vsb.cz

SubArea:

Systems of linear equations and inequalities

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Project ID:

2000019001

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0

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Four matrices are given:

(\begin{matrix} 1 & - 1 & 0 \\ 2 & 0 & 1 \\ 1 & 1 & - 1 \end{matrix}),

(\begin{matrix} 1 & - 3 & 0 \\ 2 & - 5 & 1 \\ 1 & 0 & - 1 \end{matrix}),

(\begin{matrix} - 3 & - 1 & 0 \\ - 5 & 0 & 1 \\ 0 & 1 & - 1 \end{matrix}),

(\begin{matrix} 1 & - 1 & - 3 \\ 2 & 0 & - 5 \\ 1 & 1 & 0 \end{matrix})

We want to practice Cramer's rule for solving a system of linear equations. Which of the following systems can be solved using determinants of the four matrices given above?

\begin{aligned} x - y = - 3 \\ 2 x + z = - 5 \\ x + y - z = 0 \end{aligned}

\begin{aligned} x - y - 3 z = 0 \\ 2 x - 5 z = 1 \\ x + y = - 1 \end{aligned}

\begin{aligned} - 3 x - y = 0 \\ - 5 x + z = 1 \\ y - z = - 1 \end{aligned}

\begin{aligned} x - y = 3 \\ 2 x + z = 5 \\ x + y - z = 0 \end{aligned}