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Response Details:
Let V= R4, with the inner product of u,v ε R4 defined as:
<u,v> = 2u1v1+u2v2+3u3v3+u4v4.
Find the norm of u= (1,2,-1,5) if the norm of u is defined as <u,u>.
<u,u>=|u|2
<u,v> = 2u1v1+u2v2+3u3v3+u4v4.
<u,u>=2 u1.u1 +u2.u2 +3 u3.u3+u4.u4
< (1,2,-1,5), (1,2,-1,5)> = (2).(1).(1) +(2).(2) + (3).(-1).(-1) +(5).(5)
|u|2 =2 + 4 +3 + 25
|u|2 = 34
|u| =  |