Explanation Approach: The Gaussian Elimination with Back-Substitution is as follows. Write the augmented matrix of the system of linear equations. Use elementary row operations to rewrite the augmented matrix in row-echelon form. The elementary row operations are; Interchange of two rows. Multiply a row by a nonzero constant. Add a multiple of a row to another row. Write the system of linear equations corresponding to the matrix in row-echelon form and use back-substitution to find the solution. Calculation: The quadratic function is given as, f ( x ) = a x 2 + b x + c ... ( 1 ) Consider the condition f ( 1 ) = 2 Substitute 1 for x and 2 for f ( x ) in equation ( 1 ) as, f ( x ) = a x 2 + b x + c 2 = a ( 1 ) 2 + b ( 1 ) + c 2 = a + b + c a + b + c = 2 ... ( 2 ) Consider the condition f ( 2 ) = 9 Substitute 2 for x and 9 for f ( x ) in equation ( 1 ) as, f ( x ) = a x 2 + b x + c 9 = a ( 2 ) 2 + b ( 2 ) + c 9 = 4 a + 2 b + c 4 a + 2 b + c = 9 ... ( 3 ) Consider the condition f ( 3 ) = 20 Substitute 3 for x and 20 for f ( x ) in equation ( 1 ) as, f ( x ) = a x 2 + b x + c 20 = a ( 3 ) 2 + b ( 3 ) + c 20 = 9 a + 3 b + c 9 a + 3 b + c = 20 ... ( 4 ) The coefficient matrix corresponding to the equations ( 2 ) , ( 3 ) and ( 4 ) is [ 1 1 1 4 2 1 9 3 1 ] The augmented matrix is given as, [ 1 1 1 ⋮ 2 4 2 1 ⋮ 9 9 3 1 ⋮ 20 ] Solve the matrix using the three elementary row operations as mentioned in the approach part. Perform the row operation R 1 ↔ R 3 as, [ 1 1 1 ⋮ 2 4 2 1 ⋮ 9 9 3 1 ⋮ 20 ] → [ 9 3 1 ⋮ 20 4 2 1 ⋮ 9 1 1 1 ⋮ 2 ] Perform the row operation R 2 ← R 2 − 4 9 R 1 as, [ 9 3 1 ⋮ 20 4 2 1 ⋮ 9 1 1 1 ⋮ 2 ] → [ 9 3 1 ⋮ 20 0 2 3 5 9 ⋮ 1 9 1 1 1 ⋮ 2 ] Perform the row operation R 3 ← R 3 − 1 9 R 1 as, [ 9 3 1 ⋮ 20 0 2 3 5 9 ⋮ 1 9 1 1 1 ⋮ 2 ] → [ 9 3 1 ⋮ 20 0 2 3 5 9 ⋮ 1 9 1 2 3 8 9 ⋮ − 2 9 ] Perform the row operation R 3 ← R</

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Chapter 8.1, Problem 88E

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The quadratic function f(x) that satisfies the conditions, f(1)=2, f(2)=9, f(3)=20.

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Chapter 8.1, Problem 87E

Chapter 8.1, Problem 89E

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The quadratic function f ( x ) that satisfies the conditions, f ( 1 ) = 2 , f ( 2 ) = 9 , f ( 3 ) = 20 .

Solution Summary: The author explains how the Gaussian Elimination with Back-Substitution works by rewriting the augmented matrix of the system of linear equations in row-echelon form.

Videos

To find:

The quadratic function f(x) that satisfies the conditions, f(1)=2, f(2)=9, f(3)=20.

Want to see the full answer?

Chapter 8 Solutions

The quadratic function f ( x ) that satisfies the conditions, f ( 1 ) = 2 , f ( 2 ) = 9 , f ( 3 ) = 20 .

Solution Summary: The author explains how the Gaussian Elimination with Back-Substitution works by rewriting the augmented matrix of the system of linear equations in row-echelon form.

Videos

To find: The quadratic function f(x) that satisfies the conditions, f(1)=2, f(2)=9, f(3)=20.

Want to see the full answer?

Chapter 8 Solutions

To find:

The quadratic function f(x) that satisfies the conditions, f(1)=2, f(2)=9, f(3)=20.