Determine whether the columns of the following matrices are

Determine whether the columns of the following matrices are linearly independent or linearly dependent. Justify your answers. [1 5 9 0 0 0 3 7 1] [1 3 2 -4 -6 -18 -12 24] [1 1 2 5 3 -2 12 8 0]

Solution

a.Determinant of this matrix is 0 so it is linearly dependent.

way if calculating determinant

(1(0*1-0*7))-(0(5*1-9*7))+(3(5*0-0*9))

this equals to zero.so it is linearly dependent.

b.

for this multiply column C1 by 6

we get

6. -6

18. -18

12 -12

24 -24

on adding C1 and C2 we get

0 determinant

so this is linearly dependent.

c.

we have to find determinant for this matrix

(1(0+16))-(5(0-16))+(12(-2-6))

on solving this,we get

16+80-96=0

so this is also linearly dependent.