shyyyy13
17.08.2020 •
Mathematics
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
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Ответ:
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.
Ответ: