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Mathematics-Online problems:

Interactive Problem 276: Linear System of Equations with Paramer (3x3)

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 paramer $ t$ has the system of equations
\begin{displaymath}\begin{array}{rcrcrcr} x&+ &y&+&tz& = & -1 \\ 3x&+&(t+1)\,y& + &(t-1)\,z & = & -1\\ tx & + & 2y &+& z& = & 0 \end{array}\end{displaymath}
no solution, more than one solution resp. exactly one solution?


Solution:

No solution for $ t=$ and (in ascending order),

infinitely many solutions for $ t=$ ,

exactly one solution for all other values of $ t$.
   

(Authors: Höllig/Knödler)

see also:

  automatically generated: 3/12/2018