Answer:
-8
Step-by-step explanation:
If we let x and y represent the first and second numbers, respectively, we can write the problem statement as the equations ...
We can multiply the first equation by -9 and add 4 times the second equation to get an equation in y alone:
-9(4x +5y) +4(9x +2y) = -9(-28) +4(11)
-37y = 296 . . . . . simplify
296/-37 = y = -8 . . . . . divide by the coefficient of y
The second number is -8.
The key idea of the transformation called a rotation is the moving of the plane a certain angle around a fixed point.
No they wont have the same amount of money ana has more than jose and he’s spending more and wont have enough for the whole week, while ana will have enough and she’s only wasting 4$....
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.
Is there meant to be a picture attached with this?