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.
Where’s the rest of the info??
This is called the Pythagorean theorem : a ² + b ² = c ². You can substitute any of the variable with any of the known numbers and then you all you have to do is isolate the variable. I hope that helps!!
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Question
If someone around 831,982 to 830,000 and then someone else rounds 831,982 for 800,000 who would be correct?
Answer:
Hi, There! Mika-Chan I'm here to help! :)
<em><u>First We Need to know If we're rounding to the Nearest Hundred thousand or Not.</u></em>
<u><em>So The Answer would Be 800,000 If your Going to Round to the nearest Hundred </em></u>
<u><em>But If We're rounding to The Nearest ten Thousand The Answer would be 830,000</em></u>
:D hope this Helps you!