Question

Solve the given system of equations using either Gaussian or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION.) x1 − 3x2 − 2x3 = 0 −x1 + 2x2 + x3 = 0 2x1 + 3x2 + 5x3 = 0

Answer 1

Answer:

No Solution

Step-by-step explanation:

Gaussian Elimination is a way to find the solution of matrix. The simple steps for using this method is:

1. Put the coefficients of equations in matrix form

2. Transform the Augmented Matrix in reduced Echelon form

3. The last column of matrix is your required answer

In the given system of equations:

First we augment the matrix:

$\left[\begin{array}{cccc}1&-3&-2&0\\-1&2&1&0\\2&3&5&0\end{array}\right]$

Pivoting Row 1 and performing following operations on given matrix

Row 2 + Row 1

Row 3 - 2(Row 1)

$\left[\begin{array}{cccc}1&-3&-2&0\\0&-1&-1&0\\0&9&9&0\end{array}\right]$

To pivot Row 2, Divide Row 2 by -1

$\left[\begin{array}{cccc}1&-3&-2&0\\0&1&1&0\\0&9&9&0\end{array}\right]$

Next step is to pivot Row 2 and perform operations on given matrix:

Row 1 + 3(Row 2)

Row 3 - 9(Row 2)

$\left[\begin{array}{cccc}1&0&-1&0\\0&1&1&0\\0&0&0&0\end{array}\right]$

Since, the last row has become zero therefore there is no solution to the given solution.