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Mathematics-Online problems:

Interactive Problem 317: Linear System of Equations with Parameter (3x3)

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For which values of the real parameter $ t$ has the following LSE no solution, exactly one solution, infinitely many solutions?

\begin{displaymath} \begin{array}{rcrcrcc} x_1 & + & tx_2 & + & tx_3 & = & 1\... ..._3 & = & 0\\ x_1 & + & tx_2 & + & x_3 & = & 4 \end{array} \end{displaymath}

For the parameter values $ t=$ and $ t=$ (in ascending order) has the LSE no solution, for all other real values:

i have no idea,

the LSE has exactly one solution ,

the LSE has infinitely many solutions .
   

see also:

  automatically generated: 8/11/2017