Let

be the

matrix whose columns are

, and let

be the vector whose components are the constants

. Now consider the matrix equation

Multiplying both sides by

, we have

More explicitly, we're writing

Multiply both sides by

and the left hand side can be written as

We're told that

whenever

, so we're left with

Each of

are nonzero, which means their norms are nonzero, which necessarily implies that

, and so the vectors

must necessarily be linearly independent.
Answer:
a mixed number has a whole number along with a fraction, while an improper fraction is just a fraction with a bigger number on top
Step-by-step explanation:
Answer:
<h2>Q1. d. 5(x - 4)(x - 6)</h2><h2>Q2. b. (8x - 1)(8x + 1)</h2>
Step-by-step explanation:

Answer: 1537.
Step-by-step explanation:
Formula for sample size :-

Given :
Margin of error : E= 100
Critical value of 95% confidence : 
Now, the required sample size will be :-

Hence, the minimum sample size required = 1537.