Let R^3 have the Euclidean inner product. Construct an orthonormal basis, {q1,q2

Question

Let R^3 have the Euclidean inner product. Construct an orthonormal basis, {q1,q2,q3}, using
the Gram-Schmidt process from the basis {v1,v2,v3} where
v1 = (1, 4, 0); v2 = (-2, 7, 3); v3 = (0, 0, 1):

Be sure to show all of your steps for this process.

I will give all 3500 of my points to the person who details this STEP BY STEP and seperates between each step of the process. For example, when calculating u2 and u3, please break it down into detail so i can understand whats going on.

Please upload a picture or some readable way of knowing whats going on. Thanks!

Explanation / Answer

1. Choose v3 as a starting vector. (For convenience) Normalize the vector by dividing the vector by the magnitude, making u1=(0,0,1);2. Project v2 along u1, by the formula of , where denotes the inner product. This makes the projection of v2 along u1 as 3/1*(0,0,1), making the projected vector as (0,0,3). Now subtract this projection from v2 to get the second orthogonal vector, which is (-2,7,0). Now make this vector to be a unit vector by dividing it by its magnitude. Thus, u2=(-2/

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