Answer:
Answer is 50 trust me
Step-by-step explanation:
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.
For question 13, you need to look at all the numbers that are less than 1/2 and then count the number of marks in total .
Answer: 7 B
For question 14, you need to first make an equation that suits the circumstances and the situations in this problem.
$25+$24x=$193
$24x=$168
x=7 weeks
x stands for the number of weeks that she has to wait for in order to save enough money to purchase the camera.
Answer: 7 weeks A
One form of the relation of inverse variation is y = k/x.
first step: Find the value of k: Taking the values x=5 and y = 4, 4=k/5, or k=20. Then, y = 20/x.
Next: Let y = 7 and find the corresp. value of x: 7=20/x, or 7x=20, or
x = 20/7 (answer)
The answer would be 5.491 million, but can be rounded to 5.5 million.