5. if t is a linear transformation such that dim im(t) = 5 dim ker(t) = 2 then can we determine dim dom(t)? hint: we learned that all these subspaces can be understood as certain subspaces associated to the standard matrix of t.

Yes, we can determine dim Dom(T).

Step-by-step explanation:

We are given that if T is  a linear transformation such that

dim Im(T)=5

Dim Ker(T)=2

We have to tell that we can determine   dim Dom(T)

Rank-nullity theorem:

Substitute the values then we get

Dim Dom(T)=7

Hence, we can determine dim Dom(T) by using rank- nullity theorem.

$97520

step-by-step explanation:

add 6% to the value she got from selling the house.

the given growth  function for the length of the fish (cm) is

f(m) = 5(1.07)m = 5.35m

where 

m = months

at the end of the study, the length is 9.19 cm. the  time for conducting the study is determined as

5.35m = 9.19

m = 1.7178 months

part a.

the study was performed over a time period  of about 1.72 months. therefore  the domain for  plotting the function is 0 < = m < = 1.72.

note:

if growth  continues at this rate for up to m months, then the domain would be 0< =m< =m.

part b.

the growth function is a linear function.

when m=0, f=0.

therefore the initial growth is zero, which represents the y-intercept.

part c.

assume that the growth function is valid for 0< =m< =9.

the average rate of change of the function is the slope of the linear function, which is 5.35 cm/month.