Question

Let ??, ?? = 2u1v1 + 3u2v2 + u3v3 define an inner product on R^3. Given: ?1, ?2, and ?3 are a basis for R^3. Use the Gram-Schmidt process and the inner product provided to convert this basis to an orthonormal basis. ?1 = [1,0,1] ?2 = [1,1,0] ?3 = [1,1,1] Use ?1 to make the first vector in the orthogonal basis, use ?2 for the second vector, and use ?3 to make the third vector in the orthonormal basis.

          Let ??, ?? = 2u1v1 + 3u2v2 + u3v3 define
an inner product on R^3.

Given: ?1, ?2, and ?3 are a basis for R^3.

Use the Gram-Schmidt process and the inner product
provided to convert this basis to an orthonormal basis.
?1 = [1,0,1]   ?2 = [1,1,0]   ?3 = [1,1,1]
Use ?1 to make the first vector in the orthogonal basis,
use ?2 for the second vector, and use ?3 to make the
third vector in the orthonormal basis.

Let ??, ?? = 2u1v1 + 3u2v2 + u3v3 define
an inner product on R^3.

Given: ?1, ?2, and ?3 are a basis for R^3.

Use the Gram-Schmidt process and the inner product
provided to convert this basis to an orthonormal basis.
?1 = [1,0,1] ?2 = [1,1,0] ?3 = [1,1,1]
Use ?1 to make the first vector in the orthogonal basis,
use ?2 for the second vector, and use ?3 to make the
third vector in the orthonormal basis.

Added by Amber H.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Supreeta N

08/10/2023

Step 1

To normalize U1, we need to find its norm with respect to the given inner product. Norm of U1 = √((u1,u1)) = √(2(1)(1) + 3(0)(0) + (1)(1)) = √(3) Normalized U1 = (1/√(3))[1, 0, 1] = [1/√(3), 0, 1/√(3)] Show more…

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Let ✈u, v✉ = 2u1v1 + 3u2v2 + u3v3 define an inner product on R3. Given: u1, u2, and u3 are a basis for R3. Use the Gram-Schmidt process and the inner product provided to convert this basis to an orthonormal basis. u1 = [1,0,1] u2 = [1,1,0] u3 = [1,1,1] Use u1 to make the first vector in the orthogonal basis, use u2 for the second vector, and use u3 to make the third vector in the orthonormal basis.