Gram-Schmidt Process · Linear Algebra

Linear Algebra Quiz

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INNER PRODUCT SPACES & ORTHOGONALITY

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A student is applying the Gram-Schmidt process to the basis

\{\vec{v}_1, \vec{v}_2, \vec{v}_3\}

\mathbb{R}^3

. They have correctly computed the first two orthonormal vectors,

\vec{u}_1

and

\vec{u}_2

, such that

\text{span}\{\vec{v}_1, \vec{v}_2\} = \text{span}\{\vec{u}_1, \vec{u}_2\}

. What is the correct expression for the third orthogonal (but not yet normalized) vector,

\vec{w}_3

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