for what value s of k are the columns of the given matrix li

for what value (s) of k are the columns of the given matrix linear dependent.

1 -5 3

3 -8 -5

-1 2 k

Solution

if the determinant value of the matrix = 0, then columns are linearly dependent.

taking the determinant along row3,

det(given matrix) = -1(( -5 x -5) -(-8 x 3)) - 2((1 x -5) - (3 x 3)) + k((1 x -8) - (3 x -5))

0 = -1(25+24) -2(-5-9) + k(-8+15)

0= -49+28+7k

7k = 21

k = 3.