Let ?1=(1,0,1,0) ?2=(0,−1,1,−1) ?3=(1,1,1,1) be linearly independent vectors in ℝ4. a. Apply the Gram-Schmidt algorithm to...

Let ?1=(1,0,1,0) ?2=(0,−1,1,−1) ?3=(1,1,1,1) be linearly independent vectors in ℝ4.

a. Apply the Gram-Schmidt algorithm to orthonormalise the vectors {?1,?2,?3} of vectors {?1,?2,?3}.

b. Find a vector ?4 such that {?1,?2,?3,?4} is an orthonormal basis for ℝ4 (where ℝ4 is the Euclidean space, that is, the inner product is the dot product).

Expert Solution

Colby Messinger answered 2 years ago

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