Which of the following sets form a basis of \mathbb r^4r 4 ?

1. Which of the following sets form a basis of R4?
2. Can 4 vectors be a basis for R4?
3. What is the standard basis of R4?
4. Can a set of 3 vectors form a basis of R4?

Which of the following sets form a basis of R4?

the set u is a basis of R4 if the vectors are linearly independent.

Can 4 vectors be a basis for R4?

A basis for R4 always consists of 4 vectors. (TRUE: Vectors in a basis must be linearly independent AND span.)

What is the standard basis of R4?

The vector space R4 has basis B = 1 e1, e2, e3 + e2, e4 + e1l.

Can a set of 3 vectors form a basis of R4?

Solution: A set of three vectors can not span R4. To see this, let A be the 4 × 3 matrix whose columns are the three vectors. This matrix has at most three pivot columns. This means that the last row of the echelon form U of A contains only zeros.