<span>Spain's conquest of central Mexico and the Andes made Spain the wealthiest and most powerful nation because of the abundance of gold and silver which it gained. This large amount of gold and silver it was able to obtain was sent to its national treasuries allowing it to become a threat to any other European competition.</span>
Answer:
b. Free
Explanation:
A software can be defined as a set of executable instructions (codes) or collection of data that is used typically to instruct a computer how to perform a specific task and to solve a particular problem.
Basically, softwares are categorized into two (2) main categories based on their shareability and availability, these are;
I. Shareware.
II. Open-source software.
III. Closed-source (subscription-based) software.
IV. Freeware.
A freeware software refers to a type of software application (program) that can be downloaded over the internet and used at no extra cost i.e without an end user having to pay an amount of money as fees.
Windows Movie Maker is a free video editing software that was designed (created) and developed by Microsoft Inc. This free software was developed to avail it end users the opportunity to effectively, easily and quickly create movie using picture and video files.
The answer is none of the above, i dont know how but i was just asked the same question and got it wrong so yeah lol
Solution. To check whether the vectors are linearly independent, we must answer the following question: if a linear combination of the vectors is the zero vector, is it necessarily true that all the coefficients are zeros?
Suppose that
x 1 ⃗v 1 + x 2 ⃗v 2 + x 3 ( ⃗v 1 + ⃗v 2 + ⃗v 3 ) = ⃗0
(a linear combination of the vectors is the zero vector). Is it necessarily true that x1 =x2 =x3 =0?
We have
x1⃗v1 + x2⃗v2 + x3(⃗v1 + ⃗v2 + ⃗v3) = x1⃗v1 + x2⃗v2 + x3⃗v1 + x3⃗v2 + x3⃗v3
=(x1 + x3)⃗v1 + (x2 + x3)⃗v2 + x3⃗v3 = ⃗0.
Since ⃗v1, ⃗v2, and ⃗v3 are linearly independent, we must have the coeffi-
cients of the linear combination equal to 0, that is, we must have
x1 + x3 = 0 x2 + x3 = 0 ,
x3 = 0
from which it follows that we must have x1 = x2 = x3 = 0. Hence the
vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer. The vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
