Determine if Linearly Dependent s={[[-7],[5],[1]],[[-6],[5],[0]]}

Problem

S={[[−7],[5],[1]],[[−6],[5],[0]]}

Solution

1. Identify the vectors in the set S Let (v_1)=[[−7],[5],[1]] and (v_2)=[[−6],[5],[0]]

2. Check for scalar multiples. Two vectors are linearly dependent if and only if one is a scalar multiple of the other, meaning (v_1)=c*(v_2) for some scalar c

3. Analyze the components. Looking at the third component, we see 1 = c(0),w*h*i*c*h*h*a*s(n)*o*s(o)*l*u*t*i*o*n*ƒ*o*r$.

4. Conclude based on the definition. Since neither vector is a scalar multiple of the other, the vectors are linearly independent.

Final Answer

S* is linearly independent

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