Bg 15.15

sarvasya caham hrdi sannivisto
mattah smrtir jnanam apohanam ca
vedais ca sarvair aham eva vedyo
vedanta-krd veda-vid eva caham

Word for word: 
sarvasya — of all living beings; ca — and; aham — I; hrdi — in the heart; sannivistah — situated; mattah — from Me; smrtih — remembrance; jnanam — knowledge; apohanam — forgetfulness; ca — and; vedaih — by the Vedas; ca — also; sarvaih — all; aham — I am; eva — certainly; vedyah — knowable; vedanta-krt — the compiler of the Vedanta; veda-vit — the knower of the Vedas; eva — certainly; ca — and; aham — I.

Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
I am seated in everyone’s heart, and from Me come remembrance, knowledge and forgetfulness. By all the Vedas, I am to be known. Indeed, I am the compiler of Vedanta, and I am the knower of the Vedas.

Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
The Supreme Lord is situated as Paramatma in everyone’s heart, and it is from Him that all activities are initiated. The living entity forgets everything of his past life, but he has to act according to the direction of the Supreme Lord, who is witness to all his work. Therefore he begins his work according to his past deeds. Required knowledge is supplied to him, and remembrance is given to him, and he forgets, also, about his past life. Thus, the Lord is not only all-pervading; He is also localized in every individual heart. He awards the different fruitive results. He is worshipable not only as the impersonal Brahman, the Supreme Personality of Godhead and the localized Paramatma, but as the form of the incarnation of the Vedas as well. The Vedas give the right direction to people so that they can properly mold their lives and come back to Godhead, back to home. The Vedas offer knowledge of the Supreme Personality of Godhead, Krishna, and Krishna in His incarnation as Vyasadeva is the compiler of the Vedanta-sutra. The commentation on the Vedanta-sutra by Vyasadeva in the Srimad-Bhagavatam gives the real understanding of Vedanta-sutra. The Supreme Lord is so full that for the deliverance of the conditioned soul He is the supplier and digester of foodstuff, the witness of his activity, and the giver of knowledge in the form of the Vedas and as the Supreme Personality of Godhead, Sri Krishna, the teacher of the Bhagavad-gita. He is worshipable by the conditioned soul. Thus God is all-good; God is all-merciful.

Antah-pravistah sasta jananam. The living entity forgets as soon as he quits his present body, but he begins his work again, initiated by the Supreme Lord. Although he forgets, the Lord gives him the intelligence to renew his work where he ended his last life. So not only does a living entity enjoy or suffer in this world according to the dictation from the Supreme Lord situated locally in the heart, but he receives the opportunity to understand the Vedas from Him. If one is serious about understanding the Vedic knowledge, then Krishna gives the required intelligence. Why does He present the Vedic knowledge for understanding? Because a living entity individually needs to understand Krishna. Vedic literature confirms this: yo ’sau sarvair vedair giyate. In all Vedic literature, beginning from the four Vedas, Vedanta-sutra and the Upanisads and Puranas, the glories of the Supreme Lord are celebrated. By performance of Vedic rituals, discussion of the Vedic philosophy and worship of the Lord in devotional service, He is attained. Therefore the purpose of the Vedas is to understand Krishna. The Vedas give us direction by which to understand Krishna and the process of realizing Him. The ultimate goal is the Supreme Personality of Godhead. Vedanta-sutra (1.1.4) confirms this in the following words: tat tu samanvayat. One can attain perfection in three stages. By understanding Vedic literature one can understand his relationship with the Supreme Personality of Godhead, by performing the different processes one can approach Him, and at the end one can attain the supreme goal, who is no other than the Supreme Personality of Godhead. In this verse the purpose of the Vedas, the understanding of the Vedas, and the goal of the Vedas are clearly defined.