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Lelu [443]
3 years ago
15

Chapitre 6. Proportionnalité (12) Approfondissement

Mathematics
1 answer:
brilliants [131]3 years ago
3 0
You have to do this because the answe is the 2nx
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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.      

8 0
3 years ago
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GuDViN [60]

Answer:

The diameter of Circle P is the same length as the radius of Circle Q.

Step-by-step explanation:

The radius of Circle Q is half of 52cm. So you would divide 52 by 2 and get 26cm as the radius of Circle Q. Therefore, the length of the diameter of Circle P is the same length as the radius of Circle Q.

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3 years ago
You have determined that a statistical study is biased. What does this mean? A. Errors were made in data collection. B. Particip
Natasha2012 [34]

Answer:

Participants were lead to respond in a specific way.

Explanation:

Bias (the verb) is to show influence or prejudice about a certain thing and can cause people to change how they act or what they do.

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Bill makes leather shoes. He charges $45 for a pair of women's shoes and $50 for a pair of men's shoes. He sells x pairs of wome
Kruka [31]

Answer:

Bill needs to sell 50 pairs of men’s clothes.

Step-by-step explanation:

50y = 2500

Divide by 50 on both sides

2500/50 = 50

7 0
3 years ago
help me please!!!!!! I really need help
IRINA_888 [86]

Answer:

Part A: hx2=a

Part B: 5hours

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