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If the system of linear equations 

x_{1}+2x_{2}+3x_{3}=6

x_{1}+3x_{2}+5x_{3}=9

2x_{1}+5x_{2}+ax_{3}=b

is consistent and has infinite number of solutions, then

Option: 1

a=8, b can be any real number


Option: 2

b=15, a can be any real number


Option: 3

a\epsilon R-\left ( 8 \right ) and b\epsilon R-\left ( 15 \right )


Option: 4

a=8, b=15


Answers (1)

best_answer

Forr consistent and has an infinite Number of solutions, we have to create linear equations such that it is less then Number of unknown.

Given equations are

x_{1}+2x_{2}+3x_{3}=6\;\;\;\;\;\;\;\;\;\;\;\;\ldots(1)

x_{1}+3x_{2}+5x_{3}=9\;\;\;\;\;\;\;\;\;\;\;\;\ldots(2)

2x_{1}+5x_{2}+ax_{3}=b\;\;\;\;\;\;\;\;\;\;\;\;\ldots(3)

Add eq (1) and eq (2), we will get eq (3)

we get a = 8 and b = 15

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qnaprep

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