Let A 3 1 2 1 Determine whether or not the four vectors list

Let A= [-3 -1 2 1], Determine whether or not the four vectors listed above the lineasly independent of linealy dependent.

Solution

we make matrix for A,B,C,D

if the determinant of matrix is 0,then they are linearly dependent ,otherwise not

we find that its determinant is 0,

so they are linearly dependent

aA +bB + cC + dD = 0

so -3a -6b +3c +18d = 0

-a -3 b +2c +6d = 0

2a +7b -3c -20d = 0

a -2d = 0

there can be infinite solution for this set of equation

so a set is (2,4,4,1) which satisfy above equations.

-3	-6	3	18
-1	-3	2	6
2	7	-3	-20
1	0	0	-2