Exercise · ZW-GRAM-SCHMIDT-PROCESS-006 · ★★☆ Intermediate
Apply Gram–Schmidt to \(v_1=(1,1,0)\), \(v_2=(1,0,1)\). What is \(w_2\)?
Choose one option.
Show answer
- D. \((\frac{1}{2},- \frac{1}{2},1)\)
Explanation
\(v_2\cdot w_1=1\) and \(w_1\cdot w_1=2\), so \(w_2=(1,0,1)-\tfrac12(1,1,0)=(\tfrac12,-\tfrac12,1)\); one checks \(w_2\cdot w_1=0\).
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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