1.. Let-V-be-setof-all-ordered-pairs of-real numbers and-consider•the-following addition and-scalar-multiplication-operations on u=(u1,u2)and v=(V1,V2):. *u+v="(U1 +V1 + 1,u2 + V2 +1), ku="(ku̟ ,'ku2).. a. Compute u+v•and-ku-for-u= (0,5), v= (-1,3)'and-k=5.. b. Show-that-(-1,-1)-=0. c. - Show that-k (u+v)•=ku+kv-and (k+m) u=ku+mu-fails-to-hold.

1.. Let-V-be-setof-all-ordered-pairs of-real numbers and-consider•the-following addition and-scalar-multiplication-operations on u=(u1,u2)and v=(V1,V2):. *u+v="(U1 +V1 + 1,u2 + V2 +1), ku="(ku̟ ,'ku2).. a. Compute u+v•and-ku-for-u= (0,5), v= (-1,3)'and-k=5.. b. Show-that-(-1,-1)-=0. c. - Show that-k (u+v)•=ku+kv-and (k+m) u=ku+mu-fails-to-hold.

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

1.. Let-V-be-setof-all-ordered-pairs of-real numbers and-consider•the-following
addition and-scalar-multiplication-operations on u=(u1,u2)and v=(V1,V2):.
*u+v='(u1 + •V1 + 1,u2 + V2 + 1), ku="(ku,,ku,)..
a. Compute u+v•and-ku-for-u= (0,5), v= (-1,3)'and-k=5..
b. Show that (-1,-1)-=0.
c. - Show that-k (u+v)•=ku+kv-and (k+m) u=ku+mu-fails-to-hold.

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