The total land area of the United States is about 3,483,511 square miles more than the total land area of Tennessee, which is ab
2 answers:
Total land area of United States is 3,537,438.
Step-by-step explanation:
Given,
Total land area of Tennessee = 53927
According to given statement,
Total land of United States = Land of Tennessee + 3483511
Total land area of United States is 3,537,438.
Keywords: Land area, addition
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The total area of the US is 3,537,438 square miles.
<u>SOLUTION: </u>
Given that, the total land area of the United States is about 3,483,511 square miles more than the total land area of Tennessee, which is about 53,927 square miles.
We have to write and solve an equation to find the total land area of the United States.
Now, according to the given information,
Total land area of the United States is about 3,483,511 square miles more than the total land area of Tennessee, which is about 53,927 square miles
Hence, the total area of the US is 3,537,438 square miles.
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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.