Explanation:
Since {v1,...,vp} is linearly dependent, there exist scalars a1,...,ap, with not all of them being 0 such that a1v1+a2v2+...+apvp = 0. Using the linearity of T we have that
a1*T(v1)+a2*T(v1) + ... + ap*T(vp) = T(a1v19+T(a2v2)+...+T(avp) = T(a1v1+a2v2+...+apvp) = T(0) = 0.
Since at least one ai is different from 0, we obtain a non trivial linear combination that eliminates T(v1) , ..., T(vp). That proves that {T(v1) , ..., T(vp)} is a linearly dependent set of W.
Answer:
Step-by-step explanation:
pythagoras theorem
a^2+b^2=c^2
8^2+x^2=10^2
64+x^2=100
x^2=100-64
x=
x=6 km
Answer:
30 % off
Step-by-step explanation:
12 dollars off of 40
40 (x) = 12
x = 12/40 = .3 or 30 %
Answer:
look at the point where s is the corner of the truangle, look at where the y and x intercepts
Step-by-step explanation:
S(-3, 2)
U(-1,1)
T(-2,4)
Answer:
25 minutes
Step-by-step explanation:
he runs 4 laps in 8 minutes
so he runs 1 lap is 8/4 = 2 minutes
Therefore he rub 12.5 laps in 2 * 12.5 = 25 minutes
