The complete question says: Let v, w, be vectors of [tex]\mathbb{R}^4[/tex]. Let A be a matrix with 4 columns v, w, 2v+w, v-w. What are the possible values for rank(A)?
The possible values for rank A = 2
What is a vector space?
A vector space is a space that contains vectors as well as the associative including the commutative operation of vector addition and the associative, as well as, distributive operations of vector multiplication by scalars.
From the information given:
- If v,w be the vectors in a [tex]\mathbb{R}[/tex]
where;
- A = matrix with 4 columns v, w, 2v+w, v-w, which are non-independent vectors.
However, the vectors 2v+w and v-w can be expressed as a linear combination of the given values of v and w(independent vectors).
We can conclude that the maximum no. of independent rows = 2. Hence, the possible rank of matrix A is 2.
Learn more about vector space here:
https://brainly.com/question/14563145
#SPJ12
