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.
The central tendency researcher use to describe these data is "mode".
<h3>What is mode?</h3>
The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.
Calculation of mode is done by-
- The number that appears the most frequently in a piece of data is its mode.
- Put the numbers in ascending order by least to greatest, then count the occurrences of each number to quickly determine the mode.
- The most frequent number is the mode.
- Simply counting how many times each number appears in the data set can help you identify the mode, which is the number that appears the most frequently in the data set.
- The figure with the largest total is the mode.
- Example: Since it happens most frequently, the mode for the data set [5, 7, 8, 2, 1, 5, 6, 7, 5] is 5.
To know more about the mode of the data, here
brainly.com/question/27951780
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Answer:
khv-hjsb-qwc. join in meet all
Answer:
Step-by-step explanation:
Rate = 56 gal / 7 min
= 8 gal / min
