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

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.

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m