Given that a = i - j + 2k, b = i + 2j + mk and

c = 3i + nj + k, are linearly dependent. Express m in terms of n in simplest fraction form.

Answer: m = (2n-9)/(n+3)

Can someone pls show their working and explanation? Thx a lot

~C~

1 answer

+1 1 3
-1 2 n
+2 m 1

determinant = 0
2 + 2n -3m -12 -nm +1 = 0

2n-9 -m(3+n) = 0

m = (2n-9)/(3+n)