Exercise · ZW-GRAM-SCHMIDT-PROCESS-001 · ★☆☆ Basic
Apply Gram–Schmidt to \(v_1=(1,1)\), \(v_2=(1,0)\). What is the second orthogonal vector \(w_2\)?
Choose one option.
Show answer
- B. \((\frac{1}{2},- \frac{1}{2})\)
Explanation
\(w_2=v_2-\frac{v_2\cdot w_1}{w_1\cdot w_1}w_1=(1,0)-\tfrac12(1,1)=(\tfrac12,-\tfrac12)\), and \(w_2\cdot w_1=0\). The option \((\tfrac12,\tfrac12)\) is the projection, not the remainder.
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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- ZW-GRAM-SCHMIDT-PROCESS-004 In the Gram–Schmidt process, what is taken as the first orthogonal vector w_1?
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