Graduate Exam Exercise: Determinant of Matrix B and Cross Product
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Linear Algebra proof: Determinant calculation of a 3x3 matrix and its cross product (Adjugate matrix application).
747 words
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4 minutes
Automata and Theory of Computation Learning Notes
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Core concepts of Theory of Computation, including automata, formal languages, computability, and complexity analysis.
1869 words
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9 minutes
Linear Algebra Learning Notes: Specialized for Japanese Graduate Entrance Exams
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Linear Algebra core concepts summary, including spaces, rank, Ax=b solution structures, and other exam focuses.
14007 words
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70 minutes
TOEFL Collocations Handbook (Master Edition)
2026-03-20
High-frequency authentic phrase mapping manual combining 12 universal reasons and all speaking corpora.
4193 words
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21 minutes