231k views
2 votes
Use row reduction to solve the system of equations.

Use row reduction to solve the system of equations.-example-1

1 Answer

6 votes

Answer:


x=-1223,y=-629,z=-31

Explanation:

The given systems of equations is


x-2y+z=4


3x-5y-17z=3


2x-6y+43z=-5


The augmented matrix is


\left[\begin{array}{cccc}1&-2&1&|\:\:\:\:4\\3&-5&-17&|\:\:\:\:3\\2&-6&43&|-5\end{array}\right].

We perform the following row operations to reduce the matrix to reduced row echelon form using row 1 as our pivot row.


R_2-3R_1\rightarrow R_2


R_3-2R_1\rightarrow R_3



\left[\begin{array}{cccc}1&-2&1&|\:\:\:\:\:\:\:\:\:\:4\\0&1&-20&|\:\:\:\:-9\\0&-2&41&|-13\end{array}\right]


Next, we perform the following row operations using row 2 as our pivot row to obtain,



R_1+2R_2\rightarrow R_1


R_3+2R_2\rightarrow R_3



\left[\begin{array}{cccc}1&0&-39&|-14\\0&1&-20&|\:\:-9\\0&0&1&|-31\end{array}\right]

Next, we perform the following row operations using row 3 as our pivot row to get,



R_1+39R_3\rightarrow R_1


R_2+20R_3\rightarrow R_2



\left[\begin{array}{cccc}1&0&0&|\:-1223\\0&1&0&|\:\:\:\:-629\\0&0&1&|\:\:\:\:\:\:-31\end{array}\right]

The matrix is now in the reduced row echelon form,

Therefore the solution is,



x=-1223,y=-629,z=-31


User Shannel
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories