HOW to tell if VECTORS are linearly INDEPENDENT or linearly dependent

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chapters
0:30 li o ld definition
2:26 linear combination
6:23 solution of the system of equations Gauss Jordan Method
13:36 vectors are li
MORE exercises LINEAR DEPENDENCE and INDEPENDENCE
• Dependencia e Independ...
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Theorem: Let A be an nxn matrix. Then detA ≠ 0 if and only if the columns (and rows) of A are linearly independent
Definition: Linear Dependence and Independence
Let v_1,v_2,…,v_n be n vectors in a vector space V. Then the vectors are said to be linearly dependent if there are n scalars c_1,c_2,…,c_n not all zeros such that
c_1 v_1+c_2 v_2+⋯+c_n v_n=0 ⃗
If the vectors are NOT linearly dependent, they are said to be linearly independent.
In other words:
The vectors v_1,v_2,…,v_n are L.i if solving the equation
c_1 v_1+c_2 v_2+⋯+c_n v_n=0 ⃗
It is obtained that c_1=c_2=⋯=c_n=0
Otherwise, if any of the scalars c_1,c_2,…,c_n is different from zero, then the vectors v_1,v_2,…,v_n are L.d

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[@juanjosemendezcarranza9797]

no es alreves, es linealmente dependiente si tiene infinitas soluciones y es linealmente independiente si da una solucion trivial

[@orlxndo3736]

Ambos escalares son 0, por definición si los escalares de la combinación lineal son iguales a cero, son linealmente independientes. Y como tu dices, son linealmente independientes si da una solución trivial, la única solución del sistema es la solución trivial.

[@mauriciolescano1464]

no entendi nada

[@javi_profe]

gracias por el comentario