Linear algebra. Will thumbs up if correct p5 7TFind the orthogonal projection ofonto the subspace V of R* spanned byprojv(v) =T-E, and

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Find the orthogonal projection of 0 0 onto the subspace V of R* spanned by projy(v) = , and 1-0 -8]

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 59CR

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Linear algebra. Will thumbs up if correct p5

7
T
Find the orthogonal projection of
onto the subspace V of R* spanned by
projv(v) =
T-E
, and

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution

Step 1

Orthogonal projection of a vector v onto a subspace V= $(v_{1}, v_{2}, v_{3}, . . . . . . . . . v_{n})$ whose vectors are mutually orthogonal is given by,

$p r o j_{v} (V) = \frac{v . v_{1}}{v_{1} . v_{1}} v_{1} + \frac{v . v_{2}}{v_{2} . v_{2}} v_{2} + . . . . . . . . . . . . \frac{v . v_{n}}{v_{n} . v_{n}} v_{n}$

Using this ,we have

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