A hiker leaves her camp in the morning. She walks 9 miles west then 10 miles north. Explain how you would find how far she has t
1 answer:
Answer:
About 13.45 miles ( rounded )
Step-by-step explanation:
You would use the pythagorean theorem to solve this. (+
=
)
would be one length of that triangle, we'll use 9.
would be the other length of that triangle, we'll use 10.
So, now you have to square both of them.
= 81 ( 9 x 9 )
= 100 ( 10 x 10 )
Which you will get 81 and 100. Then you add those two numbers together.
100 + 81 = 181
Now that you have 181, you have to square root 181.
With that you should get 13.45 miles. (rounded)
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Answer:
Only d) is false.
Step-by-step explanation:
Let 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 . 0 is a root of p, so we have that
.
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.