Find vectors in Orthogonal basis set spanning R4

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SUMMARY

An orthogonal basis set spanning R4 consists of four vectors, specifically v1, v2, v3, and v4. Given the vectors v1 = [−1, 2, 3, 0] and v2 = [−1, 1, −1, 0], the task is to find v3 and v4 such that they are orthogonal to both v1 and v2. The Gram-Schmidt process is the recommended method to derive these vectors, ensuring that the resulting set maintains orthogonality.

PREREQUISITES
  • Understanding of orthogonal vectors
  • Familiarity with the Gram-Schmidt process
  • Basic knowledge of vector spaces in R4
  • Ability to perform vector operations (dot product, linear combinations)
NEXT STEPS
  • Study the Gram-Schmidt orthogonalization process in detail
  • Practice finding orthogonal vectors in R3 and R4
  • Explore applications of orthogonal basis sets in linear algebra
  • Learn about the properties of vector spaces and their dimensions
USEFUL FOR

Students and educators in linear algebra, mathematicians, and anyone interested in understanding vector spaces and orthogonality in R4.

Minal
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An orthogonal basis set spanning R4 has four vectors, v1, v2, v3 and v4.
If v1 and v2 are
[ −1 2 3 0 ] and [−1 1 −1 0 ]
find v3 and v4.

Please explain this in a very simple way.
 
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Minal said:
An orthogonal basis set spanning R4 has four vectors, v1, v2, v3 and v4.
If v1 and v2 are
[ −1 2 3 0 ] and [−1 1 −1 0 ]
find v3 and v4.

Please explain this in a very simple way.

You have to find ##v_3, v_4## such that those 2 vectors are orthogonal to ##v_1, v_2## (hint: Gramm-Schmidt)
 
Minal said:
please write the formula to find v3 and v4.

You should do that yourself. Nobody is going to make your homework.
 

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