(1.1) Determine whether the system x + y + x + y = 2e³t, x + y − 3x − 3y = −e¯², is degenerate. In the degenerate case, decide whether it has no solution or infinitely many solutions. If it has no solution, explain why, else find the general form of the solutions. (1.2) Solve the system: x + x = 2y = 2t², 2x − x + y − 2y = 2t³, by using the elimination method (operator method). Hint. Eliminate y first.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.5: Cramer's Rule
Problem 35PS
Question
(1.1) Determine whether the system
x + y + x + y = 2e³t,
x + y − 3x − 3y = −e¯²,
is degenerate. In the degenerate case, decide whether it has no solution or infinitely
many solutions. If it has no solution, explain why, else find the general form of the
solutions.
(1.2) Solve the system:
x + x = 2y = 2t²,
2x − x + y − 2y = 2t³,
by using the elimination method (operator method).
Hint. Eliminate y first.
Transcribed Image Text:(1.1) Determine whether the system x + y + x + y = 2e³t, x + y − 3x − 3y = −e¯², is degenerate. In the degenerate case, decide whether it has no solution or infinitely many solutions. If it has no solution, explain why, else find the general form of the solutions. (1.2) Solve the system: x + x = 2y = 2t², 2x − x + y − 2y = 2t³, by using the elimination method (operator method). Hint. Eliminate y first.
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