Each of the following properties defines a set of real n \ n matrices. Find out which sets are dense, and which are open in the space L(R") of all linear opera- tors on R": (a) determinant 0; (b) trace is rational; (c) entries are not integers; determinant < 4; (d) 3 (e) -1 < | A | < 1 for every eigenvalue >; no real eigenvalues; (f) each real eigenvalue has multiplicity one

Q: Find f 2f + 16 = 4 f-6, 6

A:

Q: -1 (4, -4) (2, –5) (6, –5) (4, -6)

A:

Q: Suppose A = (-8,7) and AB = (4, –3). Then B = help (points)

A: Find the vector if the direction of AB. Is given

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Q: 9. Let m and a be integers such that m > 1 and (a,m)= 1. Prove that if {r1, ...,r(m)} is a reduced…

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A: In (-3,9) and  (-3,-5) x ordinate = -3 for both.So on the line joining them x is fixed.

Q: Find a + b, 2a + 3b, a|, and Ja -b|. a = (5, -12), b = (-3, -6) %3D %3D a + b 2a + 3b = |al %D la b|…

A:

Q: Find (-8, 6)· (5, 1).

A:

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A: Integral.

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A: Solve the following

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A: Given,

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Q: can you explain more about how you get fxx, fxy, and fyy

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Q: (v-4)2

A:

Q: (-3) - ( -9)

A: Given : -3--9

Q: 6a b4 (e) 18a b?

A: To simplify the algebraic expression few points we should keep in mind: i) If two numbers are in…