What do we call financial assistance for a student with demonstrated financial need to help pay for college that does not need t
2 answers:
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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:
The median is 36.8
Step-by-step explanation:
The median is the middle number in an ordered list.
We have to sort the list in increasing or decreasing order
Now we can remove the first and last numbers in each iteration until we get to the median
Answer:
Step-by-step explanation:
See attachment for the figure
Volume of pyramid can be defined as
V = 1/3 x area of the base x height.
-> Pyramid A:
Volume of Pyramid can be determined by:
V = 1/3 x (2.6cm)² x (2cm) = 4.5067 cm³
Pyramid B:
Volume of Pyramid can be determined by:
V = 1/3 x (2cm)² x (2.5cm) = 3.3333 cm³
Difference b/w two oblique pyramids: 4.5067 cm³ - 3.333 cm³ = 1.17 cm³
By Rounding the volumes to the nearest tenth of a centimeter
1.17cm³ ≈ 1.2cm³
Therefore, the difference of the volumes of the two oblique pyramids is 1.2cm³
