3) Show that the irreducible polynomials in R[T] are the following: (a) Linear polynomials, i.e. polynomials of degree 1; and (b) Quadratic polynomials, i.e. polynomials of degree 2, which do not have a real root. If g(T) is such a polynomial then g(T) = a · (T – z) · (T – z) = a · (T² + (z + z) · T + z• z), where z is a complex root of g(T), and a e R \ {0}.

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A: Since, the image contains two different problems, according to the guidelines, I am solving the…

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A: This is a problem of linear algebra. Let's solve it using the concept of linear algebra.

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A: Sol

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A:

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A:

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A: (a)Interpolating polynomial is given by

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A: a=1b=-2c=5Explanation:

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A:

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A:

Q: his is some (a) Use this

A: Given  (a) y" + 3y' + 2y = f(t), y(0)=y'(O)=0. (b)f(t) = e3t and f(t) = t.

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A:

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A: A norm is a function that assigns a non-negative length or size to each vector in a vector space.…

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A:

Q: Let B = {1, t − 3, (t − 3)² } and C = - - {1, t − 2, (t − 2)²} - be two bases for P2. The function…

A: a=1, b=-2, c=5Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Let A be invertible. Prove that At is invertible and (At)−1 = (A−1)t.

A: Given:Let A be invertible. Prove that AT is invertible and (AT)−1 = (A−1) T.

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Q: 4) Let n-1 f(T) = T" +) a; · Ti i=0 be a monic polynomial of degree n > 1 with a; E Z for all 0 < i…

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A: We take an example to satisfy this question

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A: