Homework Help: Linear Algebra

Posted by Linus on Monday, January 17, 2011 at 4:34pm.

Express the solutions of the following systems in terms of the free variables:

x1 + 3*(x2) - 2*(x3) + 2*(x5) = 0
2*(x1) + 6*(x2) - 5*(x3) - 2*(x4) + 4*(x5) - 3*(x6) = -1
5*(x3) + 10*(x4) + 15*(x6) = 5
2*(x1) + 6*(x2) + 8*(x4) + 4*(x5) + 18*(x6) = 6

Linear Algebra - EssKay, Monday, January 17, 2011 at 4:57pm
Hey Linus,

First step: simplify where you can. For example, equation 3 can be divided by 5, so you end up with (x3) + 2(x4) + 3(x6) = 1. Equation 4 can also be simplified. This will make the algebra later a little easier.

Second step: Pick an x (x1 seems to be a good one) to start solving, and begin moving around your equations.

Do you know where to go from here? (Or are you onto matrices already? If so ignore step 2 and build your matrix). If you're stuck show me what you've done so far and I'll help out!
Linear Algebra - Linus, Monday, January 17, 2011 at 5:48pm
I got:

x1 = -3*(x2) -2*(x5) + 66*(x6) - 22
x2 = free
x3 = 33*(x6) - 11
x4 = -18*(x6) + 6
x5 = free
x6 = free

Is that correct?

Answer this Question

Related Questions

Math - Find the augmented matrix for each of the following systems of linear ...
Math - Which of the following are linear equations in x1, x2 and x3? (a) x1 + ...
algebra2 - solve the equation: First: x + 3y = 5 Second: 3x - y = 5 should i use...
Calculus (Urgent!!) - Hello everyone, I need help with the following problems. ...
MATH - solve the system of linear equations using the Gauss- Jordan elimination ...
Statistics - Suppose X1;X2;...;X5 is a random sample from a n(0; variance) ...
college - Which of the following choices is a solution for: (-3-i)x1 + (1-2i)x2...
Linear Algebra - I previously posted this question under the wrong topic. Which ...
parabolas - how do i find the equaion of the following parabolas? 1)intercepts ...
Calculus - Find the partial derivative y with respect to s for the following ...

For Further Reading

First Name:
School Subject:
Answer: