Question

Negative Marks : 0
If B= {V1, V2,V3} is an orthogonal set of vectors
with respect to an inner product on a vector
space V, then the set B is​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

If a set of vectors B = {V1, V2, V3} is orthogonal with respect to an inner product on a vector space V, then the inner product of any two distinct vectors in the set will be zero. That is:

<Vi, Vj> = 0 for all i ≠ j, where i, j = 1, 2, 3

In other words, the vectors in B are mutually perpendicular to each other.

If the vectors in B are also nonzero, then the set B is an orthogonal basis for the vector space V. This means that any vector in V can be expressed as a linear combination of the vectors in B, and the coefficients in this linear combination can be uniquely determined.

Furthermore, if the vectors in B are also unit vectors (i.e., they have length 1), then the set B is an orthonormal basis for the vector space V. In this case, the coefficients in the linear combination of any vector in V with respect to B can be easily determined by taking inner products with the vectors in B.

Therefore, if a set of vectors B = {V1, V2, V3} is orthogonal with respect to an inner product on a vector space V, and the vectors in B are also nonzero, then B is an orthogonal basis for V. If the vectors in B are also unit vectors, then B is an orthonormal basis for V.


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