# Constraint Equations: Get the Answers You Need

• jhg12345
In summary, the conversation discusses finding constraint equations for the vector b to be an element of the span of three given vectors in a 4-dimensional space. The solution involves creating an augmented matrix and using row operations to eliminate entries and obtain the constraint equation.
jhg12345
Thanks so much guys

Last edited:
jhg12345 said:

## Homework Statement

Find constraint equations that b must satisfy in order to be an element of
b. V= Span ((1,0,1,1),(0,1,1,2),(1,1,1,0)

None

## The Attempt at a Solution

I get the matrix
[1 0 0 -2
0 1 0 -1
0 0 1 3]. What's the restraint equation?
Let's rename b to x, since I want to use a, b, c, and d as the coordinates of this vector.
In this problem you want to find solutions for c1, c2, and c3 so that c1<1, 0, 1, 1> + c2<0, 1, 1, 2> + c3<1, 1, 1, 0> = <a, b, c, d>.

Is that enough to get you started?

Yea, that's what I did and I got a matrix, but I can't get a matrix with a row of all zeros.

Use an augmented 4 x 4 matrix with your three vectors as the first three columns, and the coordinates a, b, c, and d as the fourth column.

From the matrix you showed, it looks like you have your three vectors as rows in a 3 x 4 matrix.

ok thanks for the help so far, but I am still stuck.

Last edited:
Use the third row to eliminate the 2 entry in the row above it. Then, use the 4th row to eliminate any nonzero entries above it.

Where is your 4th column? You need that to get your constraint equation.

Yea, I know. Thanks for the help.

## What are constraint equations?

Constraint equations are mathematical equations that represent the relationships between different variables in a system. They are used to impose restrictions or limitations on the possible values of these variables.

## Why are constraint equations important?

Constraint equations are important because they help us understand and analyze complex systems by simplifying them and making them more manageable. They also allow us to identify and solve problems or optimize processes by setting boundaries and limitations.

## How do you solve constraint equations?

Solving constraint equations involves using mathematical techniques such as substitution, elimination, or graphing to find the values of the variables that satisfy all of the equations simultaneously. This is known as finding the "feasible region" or the set of solutions that meet all of the constraints.

## What are some real-world applications of constraint equations?

Constraint equations are commonly used in fields such as physics, engineering, economics, and operations research to model and optimize various systems. For example, they can be used to design efficient transportation routes, optimize production processes, or analyze the behavior of physical systems.

## Are there any limitations to using constraint equations?

While constraint equations are a powerful tool for problem-solving, they do have some limitations. They can only be used for linear relationships between variables, and they assume that the constraints and objective functions are known and well-defined. In some cases, the assumptions made in using constraint equations may not accurately reflect the real-world scenario, leading to inaccurate results.

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