Q5Advanced Engineering Mathematics II

Question

Apply the Gram-Schmidt process to the vectors $β_{1} = (1, 0, 1)$ , $β_{2} = (1, 0, - 1)$ , and $β_{3} = (0, 3, 4)$ to obtain an orthonormal basis for $V_{3} (R)$ with the standard inner product.

Answer 1

Question

10 marks

Apply the Gram-Schmidt process to the vectors $β_{1} = (1, 0, 1)$ , $β_{2} = (1, 0, - 1)$ , and $β_{3} = (0, 3, 4)$ to obtain an orthonormal basis for $V_{3} (R)$ with the standard inner product.

Answer

Applying the Gram-Schmidt process to beta1=(1,0,1), beta2=(1,0,-1), beta3=(0,3,4) gives the orthonormal basis: e1=(1/sqrt(2),0,1/sqrt(2)), e2=(1/sqrt(2),0,-1/sqrt(2)), e3=(0,1,0).