3. (a) For each vector space V, give a basis for V and give dim V. You do not have to justify why your basis is a basis. i. Is) V = M2x2, the vector space of all 2 x 2 matrices. ii. (e) V = Span iii. V is the subspace of P3 spanned by the polynomial p(t) = 1+2t+3t³. o 2] 2 3 property that P™P =I such that A= PDP". [o (b) (B Let A = Find a diagonal matrix D and a matrix P with the

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Q: https://www.youtube.com/watch?v=pE5yxgmXMmQ&t=267s This video was given as a guide

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A:

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Q: Describe the zero vector (the additive identity) of the vector space. P3 x + ]+² +

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Q: Oa + Ob+0c + 4d la + (-1) b+ (-2) c +4d Oa + 1b + (-2) c + 5d la + (-1) b+ (-2) c + 2d 2a + 1b+…

A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d   To Find:…

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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.