One has to look at three verses 9.4, 9.5 and 15.7 to answer this question.
All this world is pervaded by Me, the Unmanifested Being. All objects
subsist in Me, but not I in them.
And yet objects do not abide in Me! Behold My mysterious Divine Power!
Source and support of all objects and yet not abiding in (i.e. limited
This whole universe owes its being to the Transcendental Godhead and
yet the forms of this universe do not contain or express Him
adequately. His absolute Reality is far above the appearance in space
The explanation of the rise of the limited phenomenal universe out of
the Absolute Godhead is traced to the power of the Divine. The Supreme
is the source of all phenomena but is not touched by them. That is the
yoga of divine power. Though He creates existence, God transcends them
to such a degree that we cannot even say that He dwells in them. Even the idea of the immanence of God is, strictly speaking, untenable.
Commentary of Gita 9.4-5 by S. Radhakrishnan in his translation of Bhagavad Gita
What does Radhakrishnan mean?
Gita 9.4-9.5 is talking from the point of view of Para-Brahman or Nirguna Brahman of Advaita. The Absolute projects this universe with its living beings. However, the Absolute so transcends the world of form that you cannot say that the Absolute dwells in us.
Now let us take a look at Gita 15.7 which is the basis of Swami Vivekananda's position.
A fragment of Myself, immortal in nature, having become the embodied
spirit in the world of living, attracts to Himself the mind and the
five senses born of Prakrti.
These verse set forth the Gita conception of the personality of man or
in fact of all jivas. The jiva is basically a spirit or part of the
Supreme Being. Immediately the logician raises the question: " How can
God, who is also the Infinite Being, have parts? The Absolute must be
So all these logical ways of putting the relation are self-defeating,
because the Infinite and the Absolute Being cannot be put into the
strait-jacket of logic without converting Spirit into matter. It is
therefore better to take the Gita statement as it is without going in
for the logician's interpretation of it. The Jiva is part of the
Infinite Spirit, just as a spark from a huge conflagration is a part
of that fire. It may be a small particle but it retains in itself all
the potentialities of the mighty Divine fire. Thus it forms the basis
of Swami Vivekananda's dictum, 'Every soul is potentially divine.'
The question whether the Infinite is not reduced to the finite if it
has parts, is mere sophistry. The Supreme Spirit is not only infinite,
but He is also omnipotent. The Omnipotent Spirit can manifest as the
many without being affected by such manifestation.
Commentary of Gita 15.7 by Swami Tapasyananda in his translation of Srimad Bhagavad Gita
How can Gita's 9.4-5 position be reconciled with its 15.7 position? It cannot be reconciled without accepting that the Infinite has parts which position is not acceptable to logicians and philosophers. So we need to take this as the Gita states and accept it as a Divine mystery incapable of being put in logical terms.
The answer to the question is both are right.