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CBSE Class 12-science Answered

find for what values of k, the equations x+y+z=1,x+2y+4z=k,x+4y+10z=k² have a solution and solve them completely in each case
Asked by peethanibindusri | 11 Nov, 2023, 05:06: PM
answered-by-expert Expert Answer
Given system of simultaneous linear equations are
 
begin mathsize 14px style x plus space y space plus space space z space space equals 1 x plus 2 y plus 4 z space space equals space k x plus 4 y plus 10 z space equals space k squared end style
 
If we write above equations in matrix form , then we have
 
begin mathsize 14px style A space X space equals B end style
 
Where  begin mathsize 14px style A space equals space open vertical bar table row 1 1 1 row 1 2 4 row 1 4 10 end table close vertical bar end style  ,   X = begin mathsize 14px style open parentheses table row x row y row z end table close parentheses end style and begin mathsize 14px style B space equals space open parentheses table row 1 row k row cell k squared end cell end table close parentheses end style
 
Condition for above system of simultaneous linear equation to have unique solution is
 
determinant of matrix A should not be zero.
 
But if we try to found the matrix of A , we get determinant zero .
 
Hence , this system of simultaneous linear equation does not have unique solution.
 
Answered by Thiyagarajan K | 11 Nov, 2023, 07:41: PM

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