# GATE Questions & Answers of Systems of linear equations

## What is the Weightage of Systems of linear equations in GATE Exam?

Total 3 Questions have been asked from Systems of linear equations topic of Linear Algebra subject in previous GATE papers. Average marks 2.00.

The rank of the matrix $\left[\begin{array}{cccc}6& 0& 4& 4\\ -2& 14& 8& 18\\ 14& -14& 0& -10\end{array}\right]$ is _______________

The following simultaneous equations

x+y+z=3
x+2y+3z=4
x+4y+kz=6

will NOT have a unique solution for k equal to

For what values of $\mathrm{\alpha }$ and $\mathrm{\beta }$ the following simultaneous equations have an infinite number of solutions?
x + y + z = 5;     x + 3y + 3z = 9;     x + 2y + $\mathrm{\alpha }$z = $\mathrm{\beta }$