- #1
franz32
- 133
- 0
I hope some can help me here.
What is the best strategy in solving 4 linear equations with five unknown variables?
What is the best strategy in solving 4 linear equations with five unknown variables?
No. of Unknown = No. of Equation
Originally posted by franz32
Hello guys! I did understand what you are talking about. =)
But not that really understand fully. I tell you what I don't
understand.
Let say D = {v1, v2, v3, v4, v5} where v1 = (1, 1, 0, -1); v2 = (0, 1, 2, 1); v3 = (1, 0, 1, -1); v4 = (1, 1, -6, -3) and v5 = (-1, -5, 1, 0). In order for me to find a basis for the subspace W = Span D of R^4, I must show that D spans R^4 right? If this fails, then, can I still find a basis for it?
(a,b,c,d) = k1v1 + k2v2+ k3v3 + k4v4 + k5v5. When I made an
augmented matrix out of it, I reached ... " 0 0 0 0 | b + c -3d - 4a.
What does it mean?
When do I know if a subspace does not span?
The purpose of solving 4 linear equations with five unknown variables is to find a set of values for the variables that satisfy all of the equations simultaneously. This allows us to determine the relationship between the variables and make predictions based on that relationship.
The steps involved in solving 4 linear equations with five unknown variables are:
1. Rearrange the equations to put all variables on one side and constants on the other.
2. Use elimination or substitution to reduce the number of equations and variables.
3. Continue this process until you have only one equation and one unknown variable left.
4. Solve for the unknown variable.
5. Substitute this value back into the other equations to find the values of the remaining variables.
Yes, a system of 4 linear equations with five unknown variables can have more than one solution. This means that there is more than one set of values for the variables that satisfy all of the equations. In this case, the system is said to be consistent and dependent.
If a system of 4 linear equations with five unknown variables has no solution, then it is said to be inconsistent. This means that there is no set of values for the variables that satisfy all of the equations simultaneously. This could happen if the equations are contradictory or if there are not enough equations to solve for all of the variables.
Solving 4 linear equations with five unknown variables has numerous applications in real life. It can be used in engineering to model and solve systems of equations in electrical circuits, in economics to analyze supply and demand relationships, and in physics to calculate the motion of objects. It can also be used in everyday life, such as determining the cost of a grocery bill with multiple items and discounts, or finding the optimal mix of ingredients for a recipe.