Exercise · ZW-GRAM-SCHMIDT-PROCESS-008 · ★★☆ Intermediate
Apply Gram–Schmidt to \(v_1=(1,0,0)\), \(v_2=(1,1,0)\), \(v_3=(1,1,1)\). What is \(w_3\)?
Choose one option.
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- A. \((0,0,1)\)
Explanation
Subtract from \(v_3\) its projections onto \(w_1=(1,0,0)\) and \(w_2=(0,1,0)\): \((1,1,1)-(1,0,0)-(0,1,0)=(0,0,1)\). Subtracting only one projection leaves \((0,1,1)\), which is not orthogonal to \(w_2\).
Review the concept: Gram–Schmidt process
A procedure that turns linearly independent vectors into an orthogonal list spanning the same subspace, by subtracting from each one its projections onto the previous ones.
\[w_k=v_k-\sum_{j
More practice problems: gram–schmidt process
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