(Solution Download) If X1 and X2 are linear spaces then their product

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)
?(x1, x2) = (ax1, ax2)
The following standard rules of arithmetic are often used in computing with linear spaces.