Final answer:
If v1, v2, v3 are linearly independent vectors in R4, then v1, v2, and v3 are also linearly independent.
Step-by-step explanation:
In linear algebra, a set of vectors is said to be linearly independent if no vector in the set can be expressed as a linear combination of the other vectors. So, if v1, v2, and v3 are linearly independent vectors in R4, it means that none of these vectors can be written as a linear combination of the others.
Now, if we consider the set of vectors v1, v2, and v3, we can see that this set is a subset of the set of vectors v1, v2, v3, and v4. Since none of the vectors v1, v2, and v3 can be expressed as a linear combination of each other, it follows that v1, v2, and v3 are also linearly independent in the larger set.
Therefore, if v1, v2, v3 are linearly independent vectors in R4, v1, v2, and v3 are also linearly independent.