The value of k can be k = 1 ,k = - 2
Determinant of a Matrix is a scalar property of that Matrix. Determinant is a special number that is defined for only square matrices (plural for matrix). Square matrix have same number of rows and columns.
Given equations:
x + y + kz = 3
x + ky + z = 7
kx + y + z = 6
we can write the above equation as matrix
=[tex]\left[\begin{array}{ccc}1&1&k\\1&k&1\\k&1&1\end{array}\right][/tex]
now, finding the determinant of the above matrix
(k - 1 ) - (1 - k) + k( 1 - k²) = 0
K - 1 - 1 + k+ k - k³ = 0
3 k - 2 - k³ = 0
k³ - 3 k + 2 = 0
(k - 1 ) ( k² + k - 2 ) = 0
( k - 1 )(k -1 )(k+2) = 0
k = 1 ,k = - 2
Hence, the value of k is k = 1 ,k = - 2.
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