If

is invertible, then we can simply choose

because for any invertible matrix

by definition we must have

.
We have

, as

which means

is non-singular and has an inverse. The inverse itself would be
Answer:
1/1000 or 0.001.
Step-by-step explanation:
10 ^-3
= 1/10^3
= 1/1000.
Answer:
Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).
Remember that the general Taylor expansion is:

for our function we have:
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = (1/2)*(1/x^3)
this is enough, now just let's write the series:

This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.
Answer:
3 3/8 seconds.
Step-by-step explanation:
When it reaches the ground h = 0 so:
54t - 16t^2 = 0
16t^2 - 54t = 0
2t(8t - 27) = 0
t = 0 or t = 27/8 (we ignore the t = 0 ) so:
t = 3 3/8 seconds.