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CBSE Class 12-science Answered

X+y+4z=6 X+2y-2z=6 λx+y+z=6  How do you find the value of λ?
Asked by tejaswinimogal12 | 26 Sep, 2023, 08:17: AM
answered-by-expert Expert Answer
The given three simultaneous linear equations are
 
begin mathsize 14px style x plus y plus 4 z space equals space 6 end style
begin mathsize 14px style x plus 2 y minus 2 z space equals space 6 end style
begin mathsize 14px style lambda x space plus space y space plus space z space equals space 6 end style
 
Above equations are written in matrix form as
 
begin mathsize 14px style A space X space equals space b end style
 
where begin mathsize 14px style A space equals open vertical bar table row 1 1 4 row 1 2 cell negative 2 end cell row lambda 1 1 end table close vertical bar space space space semicolon space space X space equals space open vertical bar table row x row y row z end table close vertical bar space space a n d space b space equals space open vertical bar table row 6 row 6 row 6 end table close vertical bar end style
In the above simultaneous linear equations , λ can have any value but by cramer's rule Determinant of matrix A should not be zero.
 
Determinant of A is ( 7 - 10 λ ) . If λ = 0.7 , then determinant of A is zero and simultaneous linear equations does not have  solution.
 
hence , λ should not be equal to 0.7 and if λ have any other value we get solution for above linear equations .
 

Answered by Thiyagarajan K | 27 Sep, 2023, 09:04: PM

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CBSE 12-science - Maths
X+y+4z=6 X+2y-2z=6 λx+y+z=6  How do you find the value of λ?
Asked by tejaswinimogal12 | 26 Sep, 2023, 08:17: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
open vertical bar table row cell left parenthesis straight b plus straight c right parenthesis hat 2 end cell ab ca row ab cell left parenthesis straight a plus straight c right parenthesis hat 2 end cell bc row ac bc cell left parenthesis straight a plus straight b right parenthesis hat 2 end cell end table close vertical bar equals 2 abc left parenthesis straight a plus straight b plus straight c right parenthesis hat 3
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