1. Use the Gauss-Jordan elimination method to determine the quadratic function whose graph passes through the points (2, 5), (1,3), and (3, 15). [5 points)
1. Use the Gauss-Jordan elimination method to determine the quadratic function whose graph passes through the points (2, 5), (1,3), and (3, 15). [5 points)
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 1CE
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![1. Use the Gauss-Jordan elimination method to determine the
quadratic function whose graph passes through the points (2, 5),
(1,3), and (3, 15).
5 points)
2. Consider the system of linear equations below.
I+ 3y = -7
r - 2y = 8.
Write the system of linear equations in the form Ax = b and
use the inverse of A to solve for x = (x, y).
(5 points)
3. Find a sequence of elementary matrices whose product is the
nonsingular matrix A =! 2
5 points]
4. Solve the system of linear equations below using Cramer's Rule.
5 points]
+: = 3
2x + y + 2z
%3D
= 7
6.x + 2y + 32 = 8.
5. Consider the vector space Pa(R), the set of all polynomial func-
tions of degree less than or equal to 2 with real coefficients.
Show that the set S = {ax? + bx + c€ P2(R) | a+b = c} is
a subspace of Pa(IR).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1dd3eeed-95c8-4f90-868d-6147cb4a49bd%2F0b6ce97b-b485-4bcd-9729-748cd4528531%2F2z9979_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Use the Gauss-Jordan elimination method to determine the
quadratic function whose graph passes through the points (2, 5),
(1,3), and (3, 15).
5 points)
2. Consider the system of linear equations below.
I+ 3y = -7
r - 2y = 8.
Write the system of linear equations in the form Ax = b and
use the inverse of A to solve for x = (x, y).
(5 points)
3. Find a sequence of elementary matrices whose product is the
nonsingular matrix A =! 2
5 points]
4. Solve the system of linear equations below using Cramer's Rule.
5 points]
+: = 3
2x + y + 2z
%3D
= 7
6.x + 2y + 32 = 8.
5. Consider the vector space Pa(R), the set of all polynomial func-
tions of degree less than or equal to 2 with real coefficients.
Show that the set S = {ax? + bx + c€ P2(R) | a+b = c} is
a subspace of Pa(IR).
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