# For which real values of t does the following system of linear equations: {tx_1+x_2+x_3=1, x_1+tx_2+x_3=1, x_1+x_2+tx_3=1

For which real values of t does the following system of linear equations:
$\left\{\begin{array}{c}t{x}_{1}+{x}_{2}+{x}_{3}=1\\ {x}_{1}+t{x}_{2}+{x}_{3}=1\\ {x}_{1}+{x}_{2}+t{x}_{3}=1\end{array}$
Have:
a) a unique solution?
b) infinitely many solutions?
c) no solutions?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Nathalie Rivers
You can write your system of equations in vector/matrix form:
$\left[\begin{array}{ccc}t& 1& 1\\ 1& t& 1\\ 1& 1& t\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$
This has now the form $Ax=b$ where $A$ is the matrix $x$ the unknown and $b$ the vector of ones. If it can be solved the solution would be $x={A}^{-1}b$. Now determining whether you can solve this by consulting the determinant of $A$ or the gaussian algorithm.
memLosycecyjz