Question Given \( f_{1}(x), f_{2}(x), f_{3}(x), f_{4}(x) \) which make up a set. Which of the following describes the set being linearly dependent? \[ \begin{array}{l} f_{2}(x)=c_{1} f_{1}(x)+c_{2} f_{3}(x)+c_{3} f_{4}(x) \\ f(x)=f_{1}(x)+2 f_{2}(x)-3 f_{3}(x)+f_{4}(x) \end{array} \] the Wonskian is not equal to zero The functions are not multiples of each other.
JEMNKI The Asker · Advanced Mathematics
Transcribed Image Text: Given \( f_{1}(x), f_{2}(x), f_{3}(x), f_{4}(x) \) which make up a set. Which of the following describes the set being linearly dependent? \[ \begin{array}{l} f_{2}(x)=c_{1} f_{1}(x)+c_{2} f_{3}(x)+c_{3} f_{4}(x) \\ f(x)=f_{1}(x)+2 f_{2}(x)-3 f_{3}(x)+f_{4}(x) \end{array} \] the Wonskian is not equal to zero The functions are not multiples of each other.
More Transcribed Image Text: Given \( f_{1}(x), f_{2}(x), f_{3}(x), f_{4}(x) \) which make up a set. Which of the following describes the set being linearly dependent? \[ \begin{array}{l} f_{2}(x)=c_{1} f_{1}(x)+c_{2} f_{3}(x)+c_{3} f_{4}(x) \\ f(x)=f_{1}(x)+2 f_{2}(x)-3 f_{3}(x)+f_{4}(x) \end{array} \] the Wonskian is not equal to zero The functions are not multiples of each other.
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QMDJTD
【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/2Since given function \( \mathrm{{{f}_{{1}}{\left({x}\right)}},{{f}_{{2}}{\left({x}\right)}},{{f}_{{{3}}}{\left({x}\right)}},{{f}_{{4}}{\left({x}\right)}}} \) are linearly dependent then option 1 will be true.ExplanationA set of vector is linearly dependent if one of them can be written as linear ... See the full answer