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My name is Ann [436]
3 years ago
6

What is the solution set of {x | x < -5} ∩ {x | x > 5}

Mathematics
1 answer:
Kisachek [45]3 years ago
5 0

Answer:

The answer is: {x | x < -5} ∩ {x | x > 5}= { }.

Step-by-step explanation:

Let us first list the elements of the first set.

{x | x < -5} reads x is an element such that x is less than -5. So we list all the integers less than -5.

{x | x < -5}= {-6,-7,-8,-9,-10,-11,-12,-13,-14,...}

Similarly, we find the elements of the second set which reads: x is an element such that, x is greater than 5.  So we list all integers greater than 5

{x | x > 5}=  {6,7,8,9,10,11,12,13,14,...}

Finally we are required to find the numbers or elements in both sets that intersect or are the same with each other.

Since no element in both sets listed above intersect each other, the solution is an empty set:

Therefore, {x | x < -5} ∩ {x | x > 5}= { }.

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3 years ago
An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false
asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1) be the characteristic polynomial of B.

a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)

b) Remember that p(\lambda)=\det(B-\lambda I). 0 is a root of p, so we have that p(0)=\det(B-0 I)=\det B=0.

c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.

d) det(B)=0 by part c) so B is not invertible.

e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.      

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3 years ago
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Step-by-step explanation:

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56/100 = 0.56

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2 years ago
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