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The answer depends on the operation that is defined on the group.

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Q: Does the set of all 2x2 with real entries and determinant 2 form a group?
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What does S R followed by a number mean?

If you mean what does something like SL(3, R) mean, it is the group of all 3X3 matrices with determinant 1, with real entries, under matrix multiplication.

What determines the nature of the roots of a quadratic equation?

The determinant.The determinant is the part under the square root of the quadratic equation and is:b2-4ac where your quadratic is of the form: ax2+bx+cIf the determinant is less than zero then you have 'no real solutions' (as the square root of a negative number is imaginary.)If the determinant is = 0, then you have one real solution (because you can discount the square root of the quadratic equation)If the determinant is greater than zero you have two real solutions as you have (-b PLUS OR MINUS the square root of the determinant) all over 2aTo find the solutions where they exist you'll need to solve the quadratic formula or use another method.

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What is the formula of bordered Hessian matrix?

The bordered hessian matrix is used for fulfilling the second-order conditions for a maximum/minimum of a function of real variables subject to a constraint. The first row and first column of the bordered hessian correspond to the derivatives of the constraint whereas the other entries correspond to the second and cross partial derivatives of the real-valued function. Other than the bordered entries, the main diagonal of the sub matrix consists of entries for the second partial derivatives. All other entries of the sub matrix off of the main diagonal correspond to all combinations of cross partials. Evaluating the determinant of the bordered hessian will allow one to determine if the function attains its maximum or minimum at the stationary points, which by the way are limited in the fact that they must both satisfy the gradient equations and the constraint.

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Is it ever possible for the domain and range in a function to have different numbers of entries for example 3 domain entries to 5 range entries or 2 range entries to 7 domain entries?

Yes. The range can have fewer number of entries.As an extreme case, consider f(x) = 3, where x is a Real number.The domain is all Real numbers - infinitely many of them, while the range is one value: 3.A function can contain one-to-one or many-to-one relationships but one-to-many relationships are not permitted. As a result, the cardinality of the range cannot be bigger than the cardinality of the domain.

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Because: Real interest rate occurs when real money demand = money supply When money supply changes, the equilibrium interest rates changes as this equation shows.

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Evergrande Real Estate Group was created in 1996.

In what country do the Huttons real estate group operate?

The Huttons Real Estate Group is a real estate company that has been in operation since January in the year of 2003. The Huttons Real Estate Group operates in Singapore.