For the following system to be consistent 4x 4y 5z 5 8x

For the following system to be consistent, 4x + 4y + 5z = 5 -8x + 9y + kz = 6

Solution

For the linear system to be consistent, 3X3 determinant should not be equal to zero

Determinant = 4 * ( 9 * (-31) + 32k) + 4(36k - 248) + 5(32 *8 - 36*9)

=> 4(-279+32k) + 144k - 992 - 340

=> -2448 + 128k + 144k

=> 272k - 2448

=> 272(k-9)

Hence for the system to be consistent, k should not be equal to 9

4	4	5
-8	9	k
36	-32	-31