Question

Select all of the statements below that are true. There is a set of 8 vectors in R6 that is linearly independent. There is a set 4 vectors in R3 that does not span R3. There is a set of 7 vectors in R4 that spans R4. > There is a set of 8 vectors in R5 that does not span R5. There is a set of 6 vectors in R4 that is linearly dependent. There is a set of 6 vectors in R7 that spans R7

Answer 1

A set of 8 vectors in R6 is linearly independent and a set of 7 vectors in R4 spans R4.

Step-by-step explanation:

The statements that are true are:

• There is a set of 8 vectors in R6 that is linearly independent.
• There is a set of 7 vectors in R4 that spans R4.

In linear algebra, linear independence is a property of a set of vectors. If a set of vectors is linearly independent, it means that none of the vectors can be written as a linear combination of the others. In this case, a set of 8 vectors in R6 is linearly independent, meaning that none of the vectors can be expressed as a combination of the others.

On the other hand, if a set of vectors spans a vector space, it means that any vector in that space can be written as a linear combination of the vectors in the set. In this case, a set of 7 vectors in R4 spans R4, meaning that any vector in R4 can be expressed as a linear combination of the 7 vectors.