Creates vectors for the span

In summary, a vector span is a set of all possible linear combinations of a given set of vectors. To create a vector span, you need to have a set of vectors and determine all possible linear combinations. The concept of vector span is important for understanding and visualizing solutions to linear equations. A vector span can only have one basis, and it has many real-world applications in fields such as physics, engineering, and computer graphics.
  • #1
karush
Gold Member
MHB
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Screenshot 2021-02-02 at 10.30.47 AM.png

ok I am trying to solve some other problems following this example but can[t see how the $z_1,z_2,z_3$ are created
I know it is pulled for REFF matrix
 
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  • #2
$z_1$ is one solution to the system of equations. It is obtained by putting $x_3=1$, $x_5=x_6=0$ and computing dependent variables $x_1$, $x_2$ and $x_4$.
 

Related to Creates vectors for the span

What is the span of a vector?

The span of a vector is the set of all possible linear combinations of that vector. In other words, it is the space that can be created by scaling and adding the vector in different directions.

How do you create vectors for the span?

To create vectors for the span, you can use a linear combination of existing vectors. This means multiplying each vector by a scalar (a number) and then adding them together. The resulting vector will be in the span of the original vectors.

Why is the span important in linear algebra?

The span is important in linear algebra because it helps us understand the dimension and structure of a vector space. It also allows us to determine whether a vector is a linear combination of other vectors or not.

Can a set of vectors have an infinite span?

Yes, a set of vectors can have an infinite span. This means that there are an infinite number of possible linear combinations of the vectors, resulting in an infinite number of vectors in the span.

How can you determine if a vector is in the span of a set of vectors?

To determine if a vector is in the span of a set of vectors, you can use the process of elimination. If you can find a linear combination of the set of vectors that equals the given vector, then it is in the span. If not, then it is not in the span.

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