LINEAR ALGEBRASOLVE BY DIRECT METHOD a) In the vector space R3, let a = (1,2,1), ß = (3,1,5), y = (3,-4,7). Show that thesubspace spanned by S = {a, ß} and T = {a,ß,y } are the same.b) Consider the basis S = {a, a2,ɑz} of R³, where a, =snip(1,1,1), az = (1,1,0) andaz = (1,0,0). Express (2, –3,5) in terms of the basis elements a,, az and az.

We can solve this by finding the reduced row echelon form. We also know that elementary row…

Answered: a) In the vector space R3, let a =…

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

SOLVE BY DIRECT METHOD

a) In the vector space R3, let a = (1,2,1), ß = (3,1,5), y = (3,-4,7). Show that the
subspace spanned by S = {a, ß} and T = {a,ß,y } are the same.
b) Consider the basis S = {a, a2,ɑz} of R³, where a, =
snip
(1,1,1), az = (1,1,0) and
az = (1,0,0). Express (2, –3,5) in terms of the basis elements a,, az and az.

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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