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4. Properties of linear spaces Consider the set of ordered pairs defined on the Cartesian...

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4. Properties of linear spaces Consider the set of ordered pairs defined on the Cartesian product V={0,1,2}{0,1,2}, i.e. pairs x=(x1,x2)V with x1{0,1,2} and x2{0,1,2}. We can also refer to the pairs as 2-dimensional vectors. We define scalar multiplication of elements in V such that for a scalar a{0,1,2}, we have ax=(ax1,ax2). Furthermore, vector addition between elements in V is defined such that xy=(x1y1,x2y2). The addition () and multiplication () operations for scalars are defined according to the following tables. i. Determine whether or not V, along with and defines a vector space (i.e., verify the 10 properties). ii. Find a subspace of V with dimension equal to 1 , and verify that it is also a vector space

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