Given a list of linearly independent vectors, the Gram-Schmidt process produces a list of orthogonal unit vectors by:

subtracting from each vector its projections onto all vectors earlier in the list, and

multiplying each vector by a scalar so that the resulting vector has norm 1.

Consider the pair of vectors \(\mathbf{v_1}=\dbinom{-2}{4}\)and \(\mathbf{v_2}=\dbinom{1}{3}\)In performing the Gram-Schmidt process on this list, \(\mathbf{v_2}\) has a projection subtracted from it and is multiplied by a scalar c. Find a value of c.

Guest Feb 12, 2022