Question 1 The curve y = ax² + bx+c passes through the points (x₁, y₁), (x2, y₂) and (x3, Y3). (i) Show that the coefficients a, b and c form the solution of the system of linear equations with the following augmented matrix: (a) (ii) X₁ X₁ 1 У1 x²²x₂ 1 2 [x3 x3 1 Y3. Use the result in Question 1(a)(i) and Gauss-Jordan elimination method to solve the values of a, b and c for which the curve y = ax² + bx+c passes through the points (0,4), (2,10) and (3,19).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 1
(a)
The curve y = ax² + bx+c passes through the points (x₁, y₁), (x₂, Y2₂) and (x3, Y3).
(i)
Show that the coefficients a, b and c form the solution of the system of linear
equations with the following augmented matrix:
(ii)
x² x₁
x²x₂
x3 x3
1 У1
1 y2
1 уз
Use the result in Question 1(a)(i) and Gauss-Jordan elimination method to solve
the values of a, b and c for which the curve y = ax² + bx + c passes through
the points (0,4), (2,10) and (3,19).
Transcribed Image Text:Question 1 (a) The curve y = ax² + bx+c passes through the points (x₁, y₁), (x₂, Y2₂) and (x3, Y3). (i) Show that the coefficients a, b and c form the solution of the system of linear equations with the following augmented matrix: (ii) x² x₁ x²x₂ x3 x3 1 У1 1 y2 1 уз Use the result in Question 1(a)(i) and Gauss-Jordan elimination method to solve the values of a, b and c for which the curve y = ax² + bx + c passes through the points (0,4), (2,10) and (3,19).
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