Given a list of linearly independent vectors

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

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 = \begin{pmatrix} -2 \\ 4 \end{pmatrix}

and

\mathbf{v}_2 = \begin{pmatrix} 1 \\ 3 \end{pmatrix}

. 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

Related theory

Dot Product
Vectors
Vectors (Precalculus)

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