If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?

if given vectors must be linearly independent.

Step-by-step explanation:

A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If , and , the linear combination is:

In other words, the following system of equations must be satisfied:

(Eq. 1)

(Eq. 2)

(Eq. 3)

By Eq. 1:

Eq. 1 in Eqs. 2-3:

(Eq. 2b)

(Eq. 3b)

By Eq. 3b:

Eq. 3b in Eq. 2b:

If if given vectors must be linearly independent.

answer are

step-by-step explanation: