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Linear algebra and geometry

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Consider the circle

Which of the following spheres contains , that is ?

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In the euclidean 3-dimensional space with a fixed cartesian system, let

us consider the sphere

and the plane of equations respectively

Which of the following statements is true?

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In the euclidean 3-dimensional space with a fixed cartesian system, let us consider the circle defined by equations

Which of the following statements is true?

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Consider the circle

Which of the following spheres contains , that is ?

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In the euclidean 2-dimensional space with a fixed cartesian system, consider the conic having equation

Which of the following statements is true?

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Consider the conics

Find the correct statement.

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In the euclidean 2-dimensional space with a fixed cartesian system, consider the conic having equation

Which of the following statements is true?

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Let , , be the space of matrices with real coefficients. Consider the linear map

 such that

where is the transpose of .

Find the correct statement.

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Let be an endomorphism with characteristic polynomial .

Which one of the following statements is true?

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Let be an endomorphism with characteristic polynomial .

Which one of the following statements is true?

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