2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2a², –1+ r+a², 1 – r + a²}, {1– 3x + 2², 1 – 3r – 20?, 1 – 2x + 32²}. В B' (a) Show that B and B' are bases of P2(R). (b) Find the coordinate matrices of p(x) = 9x² + 4x – 2 relative to the bases B and B'. (c) Find the transition matrix PB→B'-

Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

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Q: 5.- Demonstrate whether the vectors of the following vector space are linearly dependent or linearly…

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Q: Show that λis a root of char(x) if and only if there exosts a non-zero vector v in V with L(v)=λv

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Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: Show that the set of polynomials of degree 3 form a vector space. P(x) = ax³ + bx² + cx+d, a, b, c,…

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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.