Write the vector form of the general solution of the given system of linear equations. 3x_1+x_2-x_3+x_4=0 2x_1+2x_2+4x_3-6x_4=0 2x_1+x_2+3x_3-x_4=0

Tabansi 2020-12-17 Answered
Write the vector form of the general solution of the given system of linear equations.
3x1+x2x3+x4=0
2x1+2x2+4x36x4=0
2x1+x2+3x3x4=0
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Anonym
Answered 2020-12-18 Author has 108 answers
[311102246021310]
Write the augmented matrix of the coefficients and constants
[100200105000100]
Transform the matrix in its reduced row echelon form.
x1=2x4
x2=5x4
x3=0
x4=x4 free
Determine the general solution
[x1x2x3x4]=x4[2501]
Rewrite the solution in vector form
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-06-01

Find the linear approximation of the function f(x)=4x at a=0
Use L(x) to approximate the numbers 3.9 and 3.99 Round to four decimal places

asked 2021-11-16
Sugar maples are 8.4 meters tall. Telephone company plans to remove the top third of the trees.
Find the height of sugar maples after they are shortened.
asked 2020-11-06
Let G be a group. Show that GqHKG=HK for any two subgroups HGHGandKGKG.
asked 2022-01-04
If a1,a2,a3,andb1,b2,b3, are arithmetic sequences, show that a1+b1,a2+b2,a3+b3, is also an arithmetic sequence.
asked 2022-05-15
Three-variable system of simultaneous equations
x + y + z = 4
x 2 + y 2 + z 2 = 4
x 3 + y 3 + z 3 = 4
Any ideas on how to solve for ( x , y , z ) satisfying the three simultaneous equations, provided there can be both real and complex solutions?
asked 2021-10-16

Simplify each expression. Express final results without using zero or negative integers as exponents.
(y3x4)2

asked 2022-05-23
I want to know how many ways there are to choose l elements in order from a set with d elements, allowing repetition, such that no element appears more than 3 times. I've thought of the following recursive function to describe this:
C ( n 1 , n 2 , n 3 , 0 ) = 1
C ( n 1 , n 2 , n 3 , l ) = n 1 C ( n 1 1 , n 2 , n 3 , l 1 ) + n 2 C ( n 1 + 1 , n 2 1 , n 3 , l 1 ) + n 3 C ( n 1 , n 2 + 1 , n 3 1 , l 1 )
The number of ways to choose the elements is then C ( 0 , 0 , d , l ). Clearly there can be at most 3 l instances of the base case C ( n 1 , n 2 , n 3 , 0 ) = 1. Additionally, if n i = 0, that term will not appear in the expansion since zero times anything is zero.
It isn't too hard to evaluate this function by hand for very small l or by computer for small l, but I would like to find an explicit form. However, while I know how to turn recurrence relations with only one variable into explicit form by expressing them as a system of linear equations (on homogeneous coordinates if a constant term is involved) in matrix form, I don't know how a four variable equation such as this can be represented explicitly. There's probably a simple combinatorical formulation I'm overlooking. How can this function be expressed explicitly?