If X1 and X2 are linear spaces, then their product X = X1 X2 is a

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If X1 and X2 are linear spaces, then their product X = X1 × X2
is a linear space with addition and multiplication defined as follows:
(x1, x2) + (y1, y2) = (x1 + y1, x2 + y2)
α(x1, x2) = (ax1, ax2)
The following standard rules of arithmetic are often used in computing with linear spaces.
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