Q3. Let L: R2R2 be a mapping from the vector space R2 to itself defined by L(x , y)= ( 2x+y, x-3y) for each (x.y) belong to R?. Show that L is a linear operator on R² and then find the representation matrix ms(L), where S is the standard bases of R?.

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Q: Q4(a) Define the null space of an m x n matrix A and prove that it is a subspace of R"

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A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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

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A: D: P3ℂ→P3ℂ be the differential operatorDpt=dpdtrelative to the basis 1, t, t2, t3

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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.