Q-1 (a) Let V = {(a1, a2): a1, az E R}. For (a1,a2), (b1, b2) E V and cER, define (a1, a2) + (b,, b2) = (a, + 2b¡, az + 3b2) and c(a,, az) = (ca1,ca2). Is Va vector space over R with these operations? Examine all the properties and justify your answer.

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A: u=(u1,u2) , ku=(3u1,0) k=2, u=(-1,2)

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: According to our guidelines we can do only one question if multiple question are posted. Please post…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.