Linear Algebra - Cubic Equation from Given Points

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SUMMARY

The forum discussion focuses on deriving a cubic polynomial equation that passes through the specified points: (0,1), (1,0), (-1,0), and (2,-15). The equation format is defined as f(t) = a + bt + ct^2 + dt^3. A critical error identified in the user's matrix involved an incorrect value in the last column, which should have been -16 instead of -15. After correcting this mistake and addressing additional algebraic errors, the user successfully resolved the problem.

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Linear Algebra -- Cubic Equation from Given Points

Homework Statement



Find the equation to the third polynomial that flows through the given points: (0,1); (1,0); (-1,0); (2, -15).

Homework Equations



f(t) = a + bt + ct^2 + dt^4

Need to find a, b, c, and d.

The Attempt at a Solution



See attachment. When I plug my answer back in, it obviously doesn't work; however, I cannot figure out where I missed up the matrix.

Any help is greatly appreciated.
 
Last edited:
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There is an error in the last column of your third matrix. You did not subtract 1 in the last column. It should be 0 2 4 8 -16, not -15.
 


Thanks for catching that mistake. Found another algebra mistake in another matrix, but all in all, I figured everything out. Thanks again for pointing out my miscue.
 

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