2000019003

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Level:

Project ID:

2000019003

Accepted:

Clonable:

Easy:

Consider a linear system of three equations with three unknowns

x

y

z

, and with the column of the right sides:

(\begin{matrix} 5 \\ 17 \\ 12 \end{matrix})

The determinants of the following two matrices were used to solve the system by Cramer's rule:

(\begin{matrix} 2 & 5 & 1 \\ 1 & 17 & - 3 \\ 1 & 12 & - 2 \end{matrix}), (\begin{matrix} 2 & - 1 & 5 \\ 1 & 2 & 17 \\ 1 & 1 & 12 \end{matrix})

Which of the following systems could be solved in a specified way?

\begin{aligned} 2 x - y + z = 5 \\ x + 2 y - 3 z = 17 \\ x + y - 2 z = 12 \end{aligned}

\begin{aligned} 2 x + 5 y + z = - 1 \\ x + 17 y - 3 z = 2 \\ x + 12 y - 2 z = 1 \end{aligned}

\begin{aligned} 2 x - y + z = - 5 \\ x + 2 y - 3 z = - 17 \\ x + y - 2 z = - 12 \end{aligned}

\begin{aligned} 2 x + y - z = 5 \\ x - 2 y + 3 z = 17 \\ x - y + 2 z = 12 \end{aligned}

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