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Mathematics-Online problems:

Interactive Problem 391: Linear System of Equations with Parameter

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
For which values of the parameter $ t\in \mathbb{R}$ has the linear system of equations

\begin{displaymath} \begin{array}{rcrcrcr} 2x & & & - & z & = & 1 \\ -2x & + & ty & + & 2z & = & -1 \\ tx & + & 2y & & & = & -1 \end{array}\end{displaymath}

no solution, more than one solution, exactely one solution? State the solution in dependency of $ t$ if it's unique.

Solution:
For $ t=$ there are infinitely many solutions.

For $ t=$ there is no solution.

Otherwise the unique solution is

$ x$ = $ \big($ $ \,t+$ $ \big)$ $ \big/$ $ \big($ $ \,t+ 2$ $ \big)$
$ y$ = $ \big($ $ \,t+$ $ \big)$ $ \big/$ $ \big($ $ \,t+ 2$ $ \big)$
$ z$ = $ \big($ $ \,t+$ $ \big)$ $ \big/$ $ \big($ $ \,t+ 2$ $ \big)$

   

(Authors: Boßle/Knödler)

see also:

  automatically generated: 3/12/2018