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2. The general form of a cubic is p(x) = ao + a1x +a2x² + a3x³ %3D Suppose you are given the following four points in the x, y plane: (-1,4), (0, 1), (1,0), and (2, –5). Find a cubic passing through all these points. (Hint: if the cubic passes through these points, then p(-1) = 4, p(0) = 1, p(1) = 0, and p(2) = -5. Plug these values into the general form of a cubic and get a system of 4 equations with 4 unknowns: ao, a1, a2, a3. Solve this system using matrices.)

2. The general form of a cubic is p(x) = ao + a1x +a2x² + a3x³ %3D Suppose you are given the following four points in the x, y plane: (-1,4), (0, 1), (1,0), and (2, –5). Find a cubic passing through all these points. (Hint: if the cubic passes through these points, then p(-1) = 4, p(0) = 1, p(1) = 0, and p(2) = -5. Plug these values into the general form of a cubic and get a system of 4 equations with 4 unknowns: ao, a1, a2, a3. Solve this system using matrices.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 13AEXP
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2. The general form of a cubic is p(x) = ao + a1x + azx² + azx³ Suppose you are given the following four points in the x, y plane: (-1,4), (0, 1), (1,0), and (2, –5). Find a cubic passing through all these points. (Hint: if the cubic passes through these points, then p(-1) = 4, p(0) = 1, p(1) = 0, and p(2) = -5. Plug these values into the general form of a cubic and get a system of 4 equations with 4 unknowns: ao, a1, a2, az. Solve this system using matrices.)
Transcribed Image Text:2. The general form of a cubic is p(x) = ao + a1x + azx² + azx³ Suppose you are given the following four points in the x, y plane: (-1,4), (0, 1), (1,0), and (2, –5). Find a cubic passing through all these points. (Hint: if the cubic passes through these points, then p(-1) = 4, p(0) = 1, p(1) = 0, and p(2) = -5. Plug these values into the general form of a cubic and get a system of 4 equations with 4 unknowns: ao, a1, a2, az. Solve this system using matrices.)
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