help for 16 zall16 For what values of k are the columns of m

help for 16

zall-16. For what value(s) of k are the columns of matrix linearly dependent. men

Solution

The columns will be linearly dependent if

av1 + bv2 = v3

a(1,2,1,0) + b(0,-1,3,k) = (1,1,-k,-4)

a = 1

2a -b = 1

b = 2a - 1 = 1

a + 3b = -k

k = -4

Hence the value of k must be -(a+3b) = -4

Hence for value of k=-4, the columns of the matrix are linearly independent