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

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

(a) The set V of all ordered pairs (x, y) of real numbers with the 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 of M22 but scalar multiplication ∗ defined by α ∗ X = αXT , α ∈ R

Expert Solution

Colby Messinger answered 11 months ago

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