Question

Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

Three points (1,1,0), (3,1,3), and (5,3,3).

To find,

Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent​.

Solution,

We can simply prove the mathematical statement by the following process.

We know that,

To prove that three points are linearly dependent, we have to find its determinant.

Thus, for vectors (1,1,0), (3,1,3) and (5,3,3) to be linearly dependent​,

⇒ $\left[\begin{array}{ccc}1&3&5\\1&1&3\\0&3&3\end{array}\right]$ = 0

⇒ 1 ( 3 - 9 ) - 3 ( 3 - 0 ) + 5 ( 3 - 0 ) = 0

⇒ 1 (-6) - 3(3) + 5(3) = 0

⇒ -6 -9 +15 = 0

⇒ -15 +15 = 0

⇒ 0 =0 (Hence proved)

Thus, it is proved that the vectors (1,1,0), (3,1,3), and (5,3,3) are not linearly independent​. They are linearly dependent.