Answer to Question #173503 in Linear Algebra for ANJU JAYACHANDRAN

Question

7(b) Is the set of vectors {( ),3,2,1 ),1,4,3( )}2,3,2( linearly independent? Give reasons for 

the answer. (3) 

 

6 4 1 5 14 

8 9 2 7 16 

4 3 6 2 5 

6 10 15 4

Answer 1

$\text{The co-efficient matrix for the given set of vectors is}$

$\begin{pmatrix} 3 & 2 & 1 \\ 1 & 4 & 3 \\ 2 & 3 & 2 \end{pmatrix} \\$

the determinant of the matrix is

$3(8-9)-2(-4)-5=0$

$\text{Since the determinant is 0, the inverse doesn't exist, it has non-trivial solutions}$

$\text{The set of vectors is not linearly independent}$