Answer:
19
Step-by-step explanation:
M is the center of the triangle, means that MR=MQ=PM
and M is the in center of the triangle=MS=MT=MU=19
Answer:
4 eggs are left.
Step-by-step explanation:
It is actually a tricky question and the trick is that the person, who initially have 6 eggs, has broken two eggs out of them.
Those two broken eggs were then fried and later he ate those.
It is a single incident but in question it appears that 3 different incidents took place in which the person have used all 6.
So actually, he only ate 2 eggs out of 6.
Answer:
slope: -3/5
y-intercept (0,3)
x - y
0 3
5 0
Step-by-step explanation:
I just did it
Step-by-step explanation:
y -4x = -1
y = 4x -1
then y = Mx + b
m = 4
b = -1
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.