SOLUTION: Find k such that the matrix, M = [-3, 0, -3] [3, 2, 5] [-6+k, -2, -11] is singular.

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find k such that the matrix, M = [-3, 0, -3] [3, 2, 5] [-6+k, -2, -11] is singular.       Log On


   

Question 1159515: Find k such that the matrix, M =
[-3, 0, -3]
[3, 2, 5]
[-6+k, -2, -11]
is singular.
Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let the rows of the given matrix be  E1,  E2  and E3, counting from the top to the bottom.


Notice that the row  2E1 - E2 is equal to

    [-9,  -2,  -11].


It will be exactly equal to the third row,  E3,  if  -9 = -6+k, i.e. k= -3.


Then the determinant of the matrix will be zero.


ANSWER.  k = -3.

Solved.