Please help!!!!!!!!
1 answer:
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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.
Answer:
17
Step-by-step explanation:
Pythagorean theory baby! Okay so the Pythagorean theory is a² + b² = c² so lets draw a triangle and label our sides. So we know 8² + 15² = c² so I'm going to find the square root of all of our numbers. We get 64 + 225 = c² so then add 64 + 225 = 289 then I take the square root of 289 which equals 17 . This answer also makes sense because out hypotenuse should always be bigger then the legs.
I'm pretty sure thats right, Hope this helps.
