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, 17:06: PM
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](https://images.topperlearning.com/topper/tinymce/cache/cac3408cb087ba936d1d2402c2b26865.png)
If we write above equations in matrix form , then we have
![begin mathsize 14px style A space X space equals B end style](https://images.topperlearning.com/topper/tinymce/cache/74cfe256caafa49e87d94cea4e6038b8.png)
Where
, X =
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](https://images.topperlearning.com/topper/tinymce/cache/bf1b6e90e194dc7d72b3b5880f0ed6c3.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/8574a3a5cc8aca0cbe915e6487735f39.png)
![begin mathsize 14px style open parentheses table row x row y row z end table close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/67515bf2bebfb7442cbf3411bf1d43a8.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/bf1b6e90e194dc7d72b3b5880f0ed6c3.png)
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, 19:41: PM
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