Exercise · ZW-GRAM-SCHMIDT-PROCESS-003 · ★☆☆ Basic
Apply Gram–Schmidt to \(v_1=(1,-1)\), \(v_2=(2,0)\). What is \(w_2\)?
Choose one option.
Show answer
- A. \((1,1)\)
Explanation
\(\frac{v_2\cdot w_1}{w_1\cdot w_1}=\frac22=1\), so \(w_2=(2,0)-(1,-1)=(1,1)\).
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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