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.
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
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
Answer:
insurance payments every month
Answer: 19 Startroot and 24 endroot
Step-by-step explanation: