# GATE Questions & Answers of Numerical solutions of linear and non-linear algebraic equations

## What is the Weightage of Numerical solutions of linear and non-linear algebraic equations in GATE Exam?

Total 5 Questions have been asked from Numerical solutions of linear and non-linear algebraic equations topic of Numerical Methods subject in previous GATE papers. Average marks 1.60.

There is no value of x that can simultaneously satisfy both the given equations.Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the value of x that minimizes the sum of squares of the errors in the two equations. __________
2x=3
4x=1

The square root of a number N is to be obtained by applying the Newton Raphson iterations to thee quation x2-N=0.if i denotes the iteration index, the correct iterative scheme will be

In the solution of the following set of linear equations by Gauss elimination using partial pivoting

5x +y +2z =34;     4y -3z =12;   and    10x -2y +z =-4;

The pivots for elimination of x and y are

The following equation needs to be numerically solved using the Newton-Raphson method.

x3 + 4x - 9 =0

The iterative equation for this purpose is (k indicates the iteration level)