Matrices and Determinants 4 Question 12

12. If the system of linear equations

x4y+7z=g,3y5z=h,2x+5y9z=k

is consistent, then

(2019 Main, 9 Jan II)

(a) 2g+h+k=0

(b) g+2h+k=0

(c) g+h+k=0

(d) g+h+2k=0

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Answer:

Correct Answer: 12. (a)

Solution:

  1. (a) Here, D=|147035259|

=1(27+25)+4(010)+7(0+6)

[expanding along R1 ]

=240+42=0

The system of linear equations have infinite many solutions.

[ system is consistent and does not have unique solution as D=0]

D1=D2=D3=0

Now, D1=0|g47h35k59|=0

g(27+25)+4(9h+5k)+7(5h3k)=0

2g36h+20k+35h21k=0

2ghk=02g+h+k=0



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