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LenaWriter [7]
3 years ago
6

Can someone please help me on this I don't understand it

Mathematics
1 answer:
muminat3 years ago
6 0
Add all three numbers together then divide by the hours ( 24 ) . ( the answer is B ) 
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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
How do you do this? plz I really need help.
Vlada [557]
The top two answers are equivalent, while the bottom one is not. You would use distributive property in the parentheses. If both expressions are the same, they are equivalent
7 0
3 years ago
I managed to prove JMK and KNJ to be congruent. How do I find that JLK is isoceles though. Please help.
Anni [7]

Answer:

Step-by-step explanation:

A triangle is isosceles if it has two equal sides and two equal angles.

From the diagram, the two perpendicular bisectors divides each base angle into 2 equal parts.

Since the 2 lines of the the perpendicular bisectors cuts across the midpoint of the triangle, it divides both lines JL and LK equally.

This means that lines JL and LK are equal.

Triangle JLK has 3 sides, JL, LK and JK.

Since lines JL and LK are equal, then

Triangle JLK is isosceles since it has two equal sides and 2 equal angles

5 0
3 years ago
What is a monthly expense you should budget for when buying a car?
AfilCa [17]

Answer:

insurance payments every month

8 0
2 years ago
Read 2 more answers
Consider the number line with the plotted square roots.
ZanzabumX [31]

Answer: 19 Startroot and 24 endroot

Step-by-step explanation:

8 0
3 years ago
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