Linear algebra: please solve last 2 parts correctly and completely 4. Consider {a,b,c} as a generating set of a vector spacefor each of the following:a)b)c)d)äta=5355OUS 25a = (5a = 15b1-0b=1-0=b4= 1¿=52=12- (9)² = ( ² )In each case, determine the dimension of the generatedvector space (with justification).In each case, if possible, represent the vector d = (5,7,8)as a linear combination of {a,b,c}.Using your geometric knowledge, determine which ofthese generating sets represents an orthogonal basis.Transform this orthogonal basis into an orthonormalbasis ONLY by normalization and give the coordinates ofd with respect to this new basis.

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Answered: In each case, determine the dimension…

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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Linear algebra: please solve last 2 parts correctly and completely

4. Consider {a,b,c} as a generating set of a vector space
for each of the following:
a)
b)
c)
d)
ä
ta
=
5355OUS 2
5
a = (5
a = 15
b
1-0
b=
1-0
=
b
4
= 1
¿=5
2=1
2
- (9)
² = ( ² )
In each case, determine the dimension of the generated
vector space (with justification).
In each case, if possible, represent the vector d = (5,7,8)
as a linear combination of {a,b,c}.
Using your geometric knowledge, determine which of
these generating sets represents an orthogonal basis.
Transform this orthogonal basis into an orthonormal
basis ONLY by normalization and give the coordinates of
d with respect to this new basis.

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.

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