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B. Fill in the blanks Find a third column so that the matrix 1/√14 2/√√/14 1/√3 -3/√14 [1/√3 Q=1/√3 is orthogonal. Is your solution unique? Show that the rows of Q form an orthonormal basis for R³.

B. Fill in the blanks Find a third column so that the matrix 1/√14 2/√√/14 1/√3 -3/√14 [1/√3 Q=1/√3 is orthogonal. Is your solution unique? Show that the rows of Q form an orthonormal basis for R³.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 35E
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Kindly solve B B part needed By hand solution needed for B part Kindly solve all three parts correctly in the order to get positive feedback please show neat and clean work for it
A. Normalizing Apply the Gram-Schmidt process to Show that the result spans R³. *-{8·A·A) 4 S = B. Fill in the blanks Find a third column so that the matrix [1/√√3 Q=1/√3 1/√14 2/√14 1/√3 -3/√14 is orthogonal. Is your solution unique? Show that the rows of Q form an orthonormal basis for R³. C. Checking concepts Classify each statement as true or false. Make sure to prove your claim or provide a counterexample. 1. If U = Span{v1, v2,..., Un}, where {v₁, v2,..., Un} form an orthonormal set, then U is a vector space with dimension n. 2. If {v1, v2} and {u₁, u2} are bases for vector space V, then {v₁ + u₁, v2 + u2} is also a basis for V.
Transcribed Image Text:A. Normalizing Apply the Gram-Schmidt process to Show that the result spans R³. *-{8·A·A) 4 S = B. Fill in the blanks Find a third column so that the matrix [1/√√3 Q=1/√3 1/√14 2/√14 1/√3 -3/√14 is orthogonal. Is your solution unique? Show that the rows of Q form an orthonormal basis for R³. C. Checking concepts Classify each statement as true or false. Make sure to prove your claim or provide a counterexample. 1. If U = Span{v1, v2,..., Un}, where {v₁, v2,..., Un} form an orthonormal set, then U is a vector space with dimension n. 2. If {v1, v2} and {u₁, u2} are bases for vector space V, then {v₁ + u₁, v2 + u2} is also a basis for V.
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