I suppose
The vectors that span 
form a basis for 
if they are (1) linearly independent and (2) any vector in can be expressed as a linear combination of those vectors (i.e. they span ).
Compute the Wronskian determinant:
The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of is 3.
Write an arbitrary vector in as 
. Then the given vectors span if there is always a choice of scalars 
such that
which is equivalent to the system
The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives
so the vectors do span .
The vectors comprising form a basis for it because they are linearly independent.
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Common ratio = second term / first term = 12 / 8 = 1.5
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Explanation:</h2><h2>
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We know that the volume of a prism is defined by:
Substituting values:
Using function concepts, it is found that it is increasing on the interval:
(–∞, –5] ∪ [3, ∞)
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The function is given by:
The graph is given at the end of this question.
- If the function is pointing upwards, it is increasing. Otherwise, it is decreasing.
- In the graph, it can be seen that it is pointing upwards for x of -5 and less, or 3 and higher, thus, the interval is:
(–∞, –5] ∪ [3, ∞)
A similar problem is given at brainly.com/question/13539822
