Answer:
Yes the linear transformation is one to one and it maps a set of real numbers R cubed onto set of real numbers R cubed
Step-by-step explanation:
To show that the linear transformation is one to one, we must show that the columns are linearly independent columns (i.e it must have the trivial solution)
![A = \left[\begin{array}{cccc}1&-2&3&0\\-1&3&-4&0\\-5&-2&9&0\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-2%263%260%5C%5C-1%263%26-4%260%5C%5C-5%26-2%269%260%5Cend%7Barray%7D%5Cright%5D)
For the Augumented matrix A and applying Row Reduction Formula we have that
= ![\left[\begin{array}{cccc}1&-2&3&0\\0&1&-1&0\\0&0&-18&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-2%263%260%5C%5C0%261%26-1%260%5C%5C0%260%26-18%260%5Cend%7Barray%7D%5Cright%5D)
we can deductively see that 
Since the columns are linearly independent, Hence it is a one-to-one transformation and it maps a set of real numbers R cubed onto set of real numbers R cubed
Answer:
Rounded to the nearest integer, the company has a total of 82,958 employees.
Step-by-step explanation:
Given that an international company has 25,800 employees in one country, if this represents 31.1% of the companies employees, to determine how many employees does it have in total, the following calculation must be performed:
31.1 = 25,800
100 = X
100 x 25,800 / 31.1 = X
2,580,000 / 31.1 = X
82,958.1 = X
Thus, rounded to the nearest integer, the company has a total of 82,958 employees.
x = number of 1-cent stamps
y = number of 8-cent stamps
z = number of 12-cent stamps
We have 31 stamps all together, so x+y+z = 31.
"I have 4 more 1-cent stamps than 8-cent stamps" means we have the equation x = y+8. Whatever y is, add 8 to it to get x. Solve for y to get y = x-8.
You also have "twice as many one cent stamps as 12 cent stamps", so x = 2z. Solving for z gets you z = 0.5x
-------------
x+y+z = 31
x+x-8+z = 31 ... y replaced with x-8
x+x-8+0.5x = 31 ... plug in z = 0.5x
2.5x-8 = 31
2.5x = 31+8
2.5x = 39
x = 39/2.5
x = 15.6
Your teacher made a typo somewhere because we should get a positive whole number result for x (since x is a count of how many 1-cent stamps we have).
