4. Let C = {a + ib : a, b E R} be the set of complex numbers.Show that C is a vector space over R with scalar operation defined byA(a + ib)λα+ ίλb, for λ ER, a, b E R.Give a set of vectors that span C as a vector space over R.

We show vector space by property of vector space

Answered: 4. Let C = {a + ib : a, b E R} be the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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4. Let C = {a + ib : a, b E R} be the set of complex numbers. Show that C is a vector space over R with scalar operation defined by A(a + ib) λα+ ίλb, for λ ER, a, b E R. Give a set of vectors that span C as a vector space over R.