Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

Find number of solutions of the system of equations
2x+y-z=7, x-3y+2z=1,x+4y-3z=5..
Also tell the conditions to solve such martices problems.please give any short method for quick solution.
Asked by rakshitreshu1997 | 07 Sep, 2015, 07:02: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space g i v e n space s y s t e m space o f space e q u a t i o n s 2 x plus y minus z equals 7 x minus 3 y plus 2 z equals 1 x plus 4 y minus 3 z equals 5 R e w r i t i n g space t h e space a b o v e space s y s t e m space o f space e q u a t i o n s space i n space m a t r i x space f o r m comma space w e space h a v e comma open square brackets table row 2 1 cell negative 1 end cell row 1 cell negative 3 end cell 2 row 1 4 cell negative 3 end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row 7 row 1 row 5 end table close square brackets rightwards double arrow A X equals B comma space w h e r e space A equals open square brackets table row 2 1 cell negative 1 end cell row 1 cell negative 3 end cell 2 row 1 4 cell negative 3 end cell end table close square brackets comma space X equals open square brackets table row x row y row z end table close square brackets space a n d space B equals open square brackets table row 7 row 1 row 5 end table close square brackets P r e m u l t i p l y i n g space A to the power of negative 1 end exponent space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma A to the power of negative 1 end exponent cross times A cross times X equals A to the power of negative 1 end exponent cross times B rightwards double arrow I X equals A to the power of negative 1 end exponent B rightwards double arrow X equals A to the power of negative 1 end exponent B T h u s space w e space n e e d space t o space f i n d space t h e space i n v e r s e space o f space t h e space m a t r i x space A space a n d space m u l t i p l y space i t space w i t h space B. L e t space u s space f i n d space t h e space d e t e r m i n a n t space o f space A open vertical bar A close vertical bar equals open vertical bar table row 2 1 cell negative 1 end cell row 1 cell negative 3 end cell 2 row 1 4 cell negative 3 end cell end table close vertical bar space space space space space equals 2 open parentheses 9 minus 8 close parentheses minus 1 open parentheses negative 3 minus 2 close parentheses minus 1 open parentheses 4 plus 3 close parentheses space space space space space equals 2 plus 5 minus 7 equals 0 S i n c e space t h e space d e t e r m i n a n t space i s space z e r o comma space A to the power of negative 1 end exponent space d o e s space n o t space e x i s t. T h u s comma space t h e r e space i s space n o space s o l u t i o n space t o space t h e space a b o v e space s y s t e m space o f space e q u a t i o n s. H e n c e space t h e space n u m b e r space o f space s o l u t i o n space i s space z e r o.
Answered by Vimala Ramamurthy | 08 Sep, 2015, 09:15: AM
CBSE 12-science - Maths
Asked by antra1799 | 18 Mar, 2024, 07:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by rahulsharmaaps4 | 03 Jan, 2023, 10:46: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by dakarapuaditya123 | 26 Dec, 2022, 08:20: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Shaikmahboob102003 | 29 Jun, 2022, 05:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by shivamaihar25 | 03 Jul, 2021, 10:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by cheragsaxena1607 | 26 Jun, 2021, 01:18: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by varunchauhan097 | 25 Apr, 2021, 08:09: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by fizzapanda | 06 Oct, 2020, 12:30: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by ashishkohar00 | 30 Sep, 2020, 11:59: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×