Ask Questions, Get Answers
Menu
X
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
studyplans
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
mobile
exams
ask
sample papers
teach
pricing
sign-in
Download our FREE mobile app with 1000+ tests for CBSE, JEE MAIN, NEET
X
Search
Topics
Want to ask us a question?
Click here
Browse Questions
Student Questions
Ad
Home
>>
TN XII Math
>>
Applications of Matrices and Determinants
0
votes
Solve the following non-homogeneous system of linear equation by determinant method: $2x+3y=5\;,4x+6y=12 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q2
sec-a
easy
Share
asked
Mar 29, 2013
by
poojasapani_1
retagged
Sep 19, 2013
by
vijayalakshmi_ramakrishnans
Please
log in
or
register
to add a comment.
Can you answer this question?
Do not ask me again to answer questions
Please
log in
or
register
to answer this question.
1 Answer
0
votes
Toolbox:
Consistency of a system of 2 ( or 3 ) linear equations in 2 ( or 3 ) unknowns. Case 1 : If $ \Delta \neq 0$ thesystem is consistent and has a unique solution. Cramer's rule can be used. Case 2 : If $ \Delta = 0$, there are two / ( four) possibilities:
2a: If $ \Delta = 0$, and atleast one of the values $ \Delta_ x, \Delta_ y ( or \: \Delta_ z )$ is nonzero, the system is inconsistent and has no solution.
2b: If $ \Delta = 0\: and \: \Delta_x=\Delta_y ( = \Delta_z)=0$ and at least one element ( second order minor ) of $ \Delta$ is nonzero, the system is consistent with infinitely many solution. The system reduces to one equation ( two equations )
2c: If $ \Delta = 0$ and $ \Delta_x=\Delta_y = \Delta_z=0$ and all their 2 x 2 minors are 0, and $\Delta$ has atleast one nonzero element, then the system is consistent with infinitely many solutions. The system reduces to one equation.
2d: If $ \Delta = 0, \Delta_x=\Delta_y = \Delta_z=0$, all 2 x 2 minors of $ \Delta$ are zero but there is at least one 2 x 2 minor of $\Delta_x, \Delta_y \: or \: \Delta_z$ that is nonzero, then the system is inconsistent and has no solution.
Step 1
$ \Delta = \begin{vmatrix} 2 & 3 \\ 4 & 6 \end{vmatrix} = 12-12=0$
The system may or may not be consistent.
Step 2
$ \Delta x = \begin{vmatrix}5 & 3 \\ 12 & 6 \end{vmatrix} = 30-36 = -6 \neq 0$
$ \Delta = 0$ but $ \Delta x \neq 0.\: \: \therefore$ the system is inconsistent and has no solution.
answered
May 27, 2013
by
thanvigandhi_1
Please
log in
or
register
to add a comment.
Related questions
0
votes
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $ 2x-y+z=2\;,6x-3y+3z=6\;,4x-2y+2z=4$
asked
Mar 29, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q8
sec-c
medium
0
votes
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $3x+2y=5\;,x+3y=4$
asked
Mar 29, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q1
sec-b
easy
0
votes
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $x+2y+z=6\;,3x+3y-z=3\;,2x+y-2z=-3 $
asked
Mar 29, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q7
sec-c
difficult
0
votes
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $3x+y-z=2\;,2x-y+2z=6\;,2x+y-2z=-2 $
asked
Mar 29, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q6
sec-b
easy
0
votes
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $ 2x+y-z=4\;,x+y-2z=0\;,3x+2y-3z=4 $
asked
Mar 29, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q5
sec-c
easy
0
votes
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $x+y+z=4\;,x-y+z=2\;,2x+y-z=1 $
asked
Mar 29, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q4
sec-c
easy
0
votes
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $4x+5y=9\;,8x+10y=18 $
asked
Mar 29, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q3
oct-2006
oct-2009
modelpaper
sec-b
medium
Ask Question
SUBMIT QUESTION
►
Please Wait
Take Test
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
JEEMAIN
350+ TESTS
NEET
320+ TESTS
CBSE XI MATH
50+ TESTS
CBSE XII MATH
80+ TESTS
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...