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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
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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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.
Transcribed Image Text: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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