2. Find the value(s) of the parameter t for which the following system of linear equations has (a) unique solution, (b) no solution, and (c) infinitely many solutions. x - 2z =1 2x+3y-z=8 2y+(r* -2)z =t+2 10 -2 1 2 3 0 2 -2 t+2] 1 0 -0 3 o 2 r-2 1+2 -2 -2 -1 6 lo 2 r-2 1+2] 1 0 -2 2 0 0 -4t-2 a. If -4 0 or t+ ±2, the system has a unique solution. b. If t=-2, the system has no solution. Last row becomes [0 o 0 -4). c. If t= 2, the system has infinitely many solutions (see graph below) since the last row becomes [0 o o o). 100 101
2. Find the value(s) of the parameter t for which the following system of linear equations has (a) unique solution, (b) no solution, and (c) infinitely many solutions. x - 2z =1 2x+3y-z=8 2y+(r* -2)z =t+2 10 -2 1 2 3 0 2 -2 t+2] 1 0 -0 3 o 2 r-2 1+2 -2 -2 -1 6 lo 2 r-2 1+2] 1 0 -2 2 0 0 -4t-2 a. If -4 0 or t+ ±2, the system has a unique solution. b. If t=-2, the system has no solution. Last row becomes [0 o 0 -4). c. If t= 2, the system has infinitely many solutions (see graph below) since the last row becomes [0 o o o). 100 101
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 17E
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