Question

check whether the following vectors are linearly independent or not . u=(1,2,3),v=(2,5,7),w=(1,3,5)​

Answer 1

Answer:

u, v , w are not linearly independent.

Step-by-step explanation:

For three vectors to be linearly independent, their determinant must equal zero.

Forming a determinant out of the three vectors, we get

$\left[\begin{array}{ccc}1&2&3\\2&5&7\\1&3&5\end{array}\right]$

Expanding along C1, we get...

1*(25-21) -2*(10-9) + 1*(14-15)

= 4 -2-1

= 1

Since Δ ≠ 0, we can conclude that the vectors u, v, w are NOT linearly independent. They are linearly dependent on each other.

Hope it helps!!