Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
The question is incomplete. The complete question is :
Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.
[tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]
Solution :
Given :
Function : [tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]
We have to determine whether the given function is linear dependent or linearly independent for the interval [tex]$(-\infty, \infty)$[/tex].
The given function are linearly dependent because for the constants, [tex]c_1[/tex] and [tex]c_2[/tex], the equation is :
[tex]$c_1x^5 + c_23 = x^5-1$[/tex] has the solution [tex]$c_1 = 1$[/tex] and [tex]$c_2 = -\frac{1}{3}$[/tex]
Therefore,
[tex]$1x^5 + \left(-\frac{1}{3}\right)3 = x^5-1$[/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
