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Zet U= Span ([]₁[0]) subspace on product of Rs Answer the following questions basal this piven u and the use of the dot as the inner product: basis of U G Find (5) X " Film B be o Let * = [!] . Create a metrix B and use this matrix to to the corolinate vector, & of to terms of Subspace U. السحر find x in

Zet U= Span ([]₁[0]) subspace on product of Rs Answer the following questions basal this piven u and the use of the dot as the inner product: basis of U G Find (5) X " Film B be o Let * = [!] . Create a metrix B and use this matrix to to the corolinate vector, & of to terms of Subspace U. السحر find x in

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let \( U = \text{span} \left( \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} \right) \) be a subspace of \( \mathbb{R}^3 \). Answer the following questions based on this given \( U \) and the use of the dot product as the inner product: **(a)** Find a basis of \( U \). **(b)** Let \( x = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \). Create a matrix \( B \) and use this matrix to find the best coordinate vector, \( \hat{x} \), of \( x \) in terms of subspace \( U \).
Transcribed Image Text:Let \( U = \text{span} \left( \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} \right) \) be a subspace of \( \mathbb{R}^3 \). Answer the following questions based on this given \( U \) and the use of the dot product as the inner product: **(a)** Find a basis of \( U \). **(b)** Let \( x = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \). Create a matrix \( B \) and use this matrix to find the best coordinate vector, \( \hat{x} \), of \( x \) in terms of subspace \( U \).
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