Are the vectors 2+5x+3x2, 4+11x+6x2 and 1+2x+x2 linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0= (2+5x+3x2)+ (4+11x+6x2)+ (1+2x+x2).

Vectors , and are linearly independent.

Step-by-step explanation:

From Linear Algebra, we must remember that a set of vectors is linearly independent if and only if coefficients of its linear combinations are all zeroes. That is:

, where . (Eq. 1)

Where:

- i-th Polynomial of the set of vectors, dimensionless.

- i-th coefficient associated with the i-ith polynomial of the set of vectors, dimensionless.

Let , and elements of the set of vectors, whose linear combination is:

Values of coefficient are contained in the following homogeneous system of linear equations:

(Eq. 2)

(Eq. 3)

(Eq. 4)

The solution of this system is:

, ,

Which means that given set of vectors are linearly independent.

step-by-step explanation:

a and d