Let B := (b₁,b2, b3) be an orthonormal basis of R³ such that b3 = √/2 * Let V = 0 and let C₁, C2, C3 be scalars such that v = = c₁b₁ + c₂b2 + c3b3. What is c3? Round your submission (as needed) to four digits after the decimal. Remember: = 0.707106.. 3 √₂ C3 = 2 √2 = : 1.414213..., number (2 digits after decimal) ? = : 2.12132...

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 71E
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Let B := (b₁,b2, b3) be an orthonormal basis of R³ such that
1
b3 = // 2
1
Let
--0
V =
and let C₁, C2, C3 be scalars such that v = c₁b₁ + c₂b2 + c3b3.
What is c3? Round your submission (as needed) to four digits after the decimal.
2
0.707106...,
1.414213...,
√2
Remember:
0
C3 =
√2
=
number (2 digits after decimal)
3
√2
?
-
= 2.12132...
Transcribed Image Text:Let B := (b₁,b2, b3) be an orthonormal basis of R³ such that 1 b3 = // 2 1 Let --0 V = and let C₁, C2, C3 be scalars such that v = c₁b₁ + c₂b2 + c3b3. What is c3? Round your submission (as needed) to four digits after the decimal. 2 0.707106..., 1.414213..., √2 Remember: 0 C3 = √2 = number (2 digits after decimal) 3 √2 ? - = 2.12132...
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