Let K be an extension of a field F and a e K be algebraic over F. Then F[a] = F (a), where F[a] = {f(a) : f (x) e F [x]}.

Q: and

A: We will find the value of x.

Q: a (1, 0, 1), b = (2, 1, −1) and c = (1, -1, 4). Calculate |ax (b+c)].

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Q: Suppose (2, -3, 4) x (1, 7, a)= (-16, 12, 17). Determine the value of a

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Q: Verify the following identities. Be sure to show all steps in a clear and neat sequence. 1. sin x +…

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Q: Let a = (-4, 5, -2) and 6=(-1,0, 4). Find à x b.

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Q: y" - y' - 12 y = e^(x/3)-e^(-x/3) A) Find the complementary solution of this homogeneous equation B)…

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Q: 5V2 + 6/64

A: We need to find the solution of 525+6645

Q: Could you please expand on how you found the linear combinations?

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Q: What is x?

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Q: If A=(7,8) and B=(2,4,6) find A x B

A: Explanation of the answer is as follows

Q: where is the res

A: We can find rest parts .

Q: Show that the sum of a positive number and its reciprocal is at least 2.

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Q: Compute/x²dx 2. using trog

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Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: Complete the sentence below. Iff is a one-to-one function and f(3) = 6, then f(6) = If f is a…

A: One one functions

Q: 20/√3

A: Given : 20/√3              Because √3 = 1.73205.....              We taka approximate value of √3 =…

Q: Where did the C come from

A: Here the C stands for “combinations”. In general, if we want to choose r objects from a total of n…

Q: If a variable, lets say a, is >0, does that mean a goes to infinity?

A: No, this does not imply that a variable, like a, goes to infinity only because it is bigger than 0.

Q: Secza (3tan 2a - 4seczx blx

A: Given : ∫sec(2x)(3tan(2x)−4sec(2x))dx