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25.07.2020 •
Mathematics
Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The set where p1(t) = t, p2(t) = t2, p3(t) = 2t + 3t2 C: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t + t2
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Ответ:
The set of vectors A and C are linearly independent.
Step-by-step explanation:
A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:
, and :
The following system of linear equations is obtained:
Whose solution is , which means that the set of vectors is linearly independent.
, and
The following system of linear equations is obtained:
Since the number of variables is greater than the number of equations, let suppose that , where . Then, the following relationships are consequently found:
It is evident that and are multiples of , which means that the set of vector are linearly dependent.
, and
The following system of linear equations is obtained:
Whose solution is , which means that the set of vectors is linearly independent.
The set of vectors A and C are linearly independent.
Ответ:
360 divided by 5 equal pieces equals to 72 a whole circle is 360 degrees
Step-by-step explanation: