Determine if Linearly Dependent s={[[6],[2],[1]],[[4],[-3],[1]]}

Problem

S={[[6],[2],[1]],[[4],[−3],[1]]}

Solution

1. Identify the number of vectors in the set. The set S contains two vectors, (v_1) and (v_2)

2. Recall the condition for linear dependence of two vectors. A set of two vectors is linearly dependent if and only if one vector is a scalar multiple of the other.

3. Set up the scalar equation to check for a constant k such that (v_1)=k*(v_2)

[[6],[2],[1]]=k*[[4],[−3],[1]]

4. Solve for k using the individual components. From the third component, we have 1 = k(1),w*h*i*c*h*i*m*p*l*i*e*s() = 1$.

5. Verify the scalar for the other components. For the first component, 6 = 1(4)i*s(ƒ)*a*l*s(e).F*o*r*t*h*e*s(e)*c*o*n*d(c)*o*m*p*o*n*e*n*t, = 1(-3)$ is false.

6. Conclude that since no such scalar k exists, the vectors are not multiples of each other. Therefore, the set is linearly independent.

Final Answer

S=Linearly Independent

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