Vandermonde Determinant Properties
Not what you're looking for?
Please show complete steps for the question on Vandermonde determinant properties attached.
Let x1, c2, x3, and x4 be real numbers.
(i) Compute the determinant of [1 x1 x1^2 x1^3; 1 x2 x2^2 x3^3; 1 x3 x3^2 x3^3; 1 x4 x4^2 x4^3]
(ii) Explain briefly and concisely while the given matrix is nonsingular (invertible, or has inverse) if the real numbers x1, x2, x3 and x4 are distinct.
(iii) Explain why we can conclude from the preceding question, that through given four points (x1, y1), (x2, y2), (x3, y3), (x4, y4) on the plane with distinct abscissa x1, x2, x3 nd x4, we can draw exactly one cubic curve given by an equation y=ax^3 + bx^2 + cx + d, where a, b, c and d are real numbers.
Purchase this Solution
Solution Summary
This solution attaches a Word file showing the calculations necessary to complete this question of the Vandermonde determinant and using its properties.
Solution Preview
Please see the attachment for step by step calculations for the problems.
Good luck.
See below for a condensed version of the solution.
Solution: the determinant is called Vandermonde's determinant and the ...
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.