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Find a basis of the subspace of Rª that consists of all vectors perpendicular to both 1 1 and -6 2 마 Basis:

Find a basis of the subspace of Rª that consists of all vectors perpendicular to both 1 1 and -6 2 마 Basis:

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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**Topic: Basis of a Subspace** **Objective:** Find a basis of the subspace of \(\mathbb{R}^4\) that consists of all vectors perpendicular to both given vectors. **Given Vectors:** - \(\begin{bmatrix} 1 \\ 0 \\ -6 \\ -2 \end{bmatrix}\) - \(\begin{bmatrix} 0 \\ 1 \\ -7 \\ 2 \end{bmatrix}\) **Problem Statement:** Determine a basis for the subspace of \(\mathbb{R}^4\) such that the basis vectors are perpendicular to the provided vectors. **Answer:** - **Basis:** \(\{ \boxed{\phantom{0}} \}\) This problem involves finding vectors that are orthogonal to the two given vectors, thus determining a subspace in \(\mathbb{R}^4\). The basis consists of vectors that satisfy the condition of orthogonality to both provided vectors.
Transcribed Image Text:**Topic: Basis of a Subspace** **Objective:** Find a basis of the subspace of \(\mathbb{R}^4\) that consists of all vectors perpendicular to both given vectors. **Given Vectors:** - \(\begin{bmatrix} 1 \\ 0 \\ -6 \\ -2 \end{bmatrix}\) - \(\begin{bmatrix} 0 \\ 1 \\ -7 \\ 2 \end{bmatrix}\) **Problem Statement:** Determine a basis for the subspace of \(\mathbb{R}^4\) such that the basis vectors are perpendicular to the provided vectors. **Answer:** - **Basis:** \(\{ \boxed{\phantom{0}} \}\) This problem involves finding vectors that are orthogonal to the two given vectors, thus determining a subspace in \(\mathbb{R}^4\). The basis consists of vectors that satisfy the condition of orthogonality to both provided vectors.
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