At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
The solution for the given system of equation is (x,y,z) is = (0 , (3-4t) , t) .
In the question ,
it is given that the system of equations are ,
3x + 3y + 12z = 9
x + y + 4z = 3
2x + 5y + 20z = 15
-x + 2y + 8z = 6
we have to solve the equations for x, y , z.
writing the given equations in augmented matrix form ,
we get ,
[tex]\left[\begin{array}{ccc}3&3&12\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}9\\3\\15\\6\end{array}\right][/tex]
Applying the operation , R₁/3 ⇒ R₁
[tex]\left[\begin{array}{ccc}1&1&4\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\3\\15\\6\end{array}\right][/tex]
Applying the row operation , R₂ - R₁ ⇒ R₂ .
[tex]\left[\begin{array}{ccc}1&1&4\\0&0&0\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\0\\15\\6\end{array}\right][/tex]
After applying more row operations , in the above matrix ,
to make the lower triangle matrix 0 ,
we get ,
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&4\\0&0&0\\0&0&0\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0\\3\\0\\0\end{array}\right][/tex]
The above result can be expressed as x = 0,
and y + 4z = 3 .
So , the system of equations have infinite solutions .
So , the solution x, y, and z expressed in terms of the parameter t is
(0 , (3-4t) , t) .
Therefore , the solution is (x,y,z) is = (0 , (3-4t) , t) .
Learn more about Solutions here
https://brainly.com/question/17025878
#SPJ4
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
