# Thread: condition for linearly dependent

1. ## condition for linearly dependent

Let
U=a₁I+b₁X+c₁Y+d₁XY
V=a₂I+b₂X+c₂Y+d₂XY
W=a₃I+b₃X+c₃Y+d₃XY
Now if I,U,V, and W are linearly dependent, then how we can write
det of matrix

b₁ c₁ d₁
b₂ c₂ d₂
b₃ c₃ d₃
=0, plz explain

2. Originally Posted by maken83
Let
U=a₁I+b₁X+c₁Y+d₁XY
V=a₂I+b₂X+c₂Y+d₂XY
W=a₃I+b₃X+c₃Y+d₃XY
Now if I,U,V, and W are linearly dependent, then how we can write
det of matrix

b₁ c₁ d₁
b₂ c₂ d₂
b₃ c₃ d₃
=0, plz explain
The det of a matrix is zero if any two or more rows are multiples of each other or if there is a row or column of all zeros.

What does the def of lin. dep. say?