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Exercise 15

Avg difficulty 3.0

Is {(x,y)∣x,y∈R}\{\hskip 1.00006pt(x,y)\mid x,y\in\mathbb{R}\hskip 1.00006pt\} a vector space under these operations?

  • (x1,y1)+(x2,y2)=(x1+x2,y1+y2)(x_{1},y_{1})+(x_{2},y_{2})=(x_{1}+x_{2},y_{1}+y_{2}) and r⋅(x,y)=(rx,y)r\cdot(x,y)=(rx,y)

  • (x1,y1)+(x2,y2)=(x1+x2,y1+y2)(x_{1},y_{1})+(x_{2},y_{2})=(x_{1}+x_{2},y_{1}+y_{2}) and r⋅(x,y)=(rx,0)r\cdot(x,y)=(rx,0)

Hefferon, Linear Algebra, Vector Spaces, Definition and Examples, Exercise 15

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.