To obtain the matrix in reduced row-echelon form, apply elementary row operations until every column that has a leading 1 has zeros in every position above and below its leading 1. Perform the operations (R2 - 4R1) on R2 and (R3 - 9R1) on R3. 1 1 0 -2 -3 -2 -3 : 5 5 R2 - 4R1 → R3 - 9R1 → 0 -6 : 12 V -8 12 step 2 Perform the operation (-R2) on R2. 1 -2 0 1 3 : -5/2 V 2 0 -6 -8 : 12 Perform the operation (R3 + 6R2) on R3. 1 1 3 0 1 2 R3 + 6R2 0 0 1 ... .. 1.
To obtain the matrix in reduced row-echelon form, apply elementary row operations until every column that has a leading 1 has zeros in every position above and below its leading 1. Perform the operations (R2 - 4R1) on R2 and (R3 - 9R1) on R3. 1 1 0 -2 -3 -2 -3 : 5 5 R2 - 4R1 → R3 - 9R1 → 0 -6 : 12 V -8 12 step 2 Perform the operation (-R2) on R2. 1 -2 0 1 3 : -5/2 V 2 0 -6 -8 : 12 Perform the operation (R3 + 6R2) on R3. 1 1 3 0 1 2 R3 + 6R2 0 0 1 ... .. 1.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:To obtain the matrix in reduced row-echelon form, apply elementary row operations until every column that
has a leading 1 has zeros in every position above and below its leading 1.
Perform the operations (R2
AR:)
on R2 and (R3
on R3.
9R1
1
1.
1
-2
-2 -3 V
-3 :
R2 - 4R1
R3 - 9R1
0 -6
: 12
-8
12
Step 2
Perform the operation (-R2) on R2.
1.
1
-2
3
: -5/2
1.
2
0 -6 -8:
12
Perform the operation (R3 + 6R2)
1 1
1:
-2
3
0 1
R3 + 6R2
0 0 1:
Transcribed Image Text:Use a system of equations to find the quadratic function f(x) = ax2 + bx + c that satisfies the equations.
Solve the system using matrices.
f(1) = -2, f(2) = -3, f(3) = -6
Step 1
The given quadratic function is f(x) = ax? + bx + c.
It is given that f(1) = -2, f(2) = -3, and f(3) = -6.
Substitute x = 1, x = 2, and x = 3 into f(x) = ax2 + bx + c to form the system of linear equations.
%3D
f(1) = a + b + c = -2
f(2)
= 4a + 2b + c = -3
f(3) = 9a + 3b + c = -6
a + b + c = -2
Therefore, the obtained system of equations is {4a + 2b + c = -3.
9а + 3b + с %3D -6
Write the associated augmented matrix for this system.
1 1 1: -2
4 2 1: -3
9 3 1: -6
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