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Determine if the following sets are real vector spaces with the indicated operations. (a) The set V...

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Advance Math

Determine if the following sets are real vector spaces with theindicated operations.

(a) The set V of all ordered pairs (x, y) of real numbers withthe addition defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2 +1) and scalar multiplication defined by α(x, y) = (αx, αy + α − 1),α ∈ R

(b) The set V of all 2 × 2 real matrices X with the addition ofM22 but scalar multiplication ∗ defined by α ∗ X = αXT , α ∈ R

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