How can I find expansion coefficients of the y vector in a given basis?

1. How do you find the basis of a vector?
2. How do you determine if a set is a basis for R3?
3. How do you determine if a set of vectors form a basis?
4. How do you find the dimension and basis of a vector space?

How do you find the basis of a vector?

Let V be a subspace of Rⁿ for some n. A collection B = v ₁, v ₂, …, v _r of vectors from V is said to be a basis for V if B is linearly independent and spans V. If either one of these criterial is not satisfied, then the collection is not a basis for V.

How do you determine if a set is a basis for R3?

The set has 3 elements. Hence, it is a basis if and only if the vectors are independent. Since each column contains a pivot, the three vectors are independent. Hence, this is a basis of R3.

How do you determine if a set of vectors form a basis?

As a result, to check if a set of vectors form a basis for a vector space, one needs to check that it is linearly independent and that it spans the vector space. If at least one of these conditions fail to hold, then it is not a basis.

How do you find the dimension and basis of a vector space?

Remark: If S and T are both bases for V then k = n. This says that every basis has the same number of vectors. Hence the dimension is will defined. The dimension of a vector space V is the number of vectors in a basis.