Determine if Linear

Problem

p*[[1],[5],[8]]=[[41/14],[26/14],[101/14]]

Solution

1. Identify the goal, which is to determine if there exists a scalar p such that the vector equation holds true.

2. Set up the system of equations by multiplying the scalar p by each component of the first vector.

p(1)=41/14

p(5)=26/14

p(8)=101/14

3. Solve for p using the first equation.

p=41/14

4. Check for consistency by substituting p=41/14 into the second equation.

5*(41/14)=205/14

5. Compare the result to the second component of the target vector.

205/14≠26/14

6. Conclude that since the value of p is not consistent across all components, no such scalar exists.

Final Answer

p*[[1],[5],[8]]≠[[41/14],[26/14],[101/14]]

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