21.3.4 - Transpose
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Practice Questions
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What is the transpose of the matrix [[1, 2], [3, 4]]?
💡 Hint: Remember to switch rows and columns.
If C = [[5, 6, 7]], what is C^T?
💡 Hint: Think about how you can represent a row as a column.
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Interactive Quizzes
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What does the transpose of a matrix do?
💡 Hint: Think about the arrangement of elements.
True or False: The transpose of the transpose of a matrix returns the same matrix.
💡 Hint: Recall the property of double transposition.
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Challenge Problems
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Given a matrix F = [[1, 0, 2], [3, 4, 5]], compute F^T and verify the property (F^T)^T = F.
💡 Hint: Always switch the rows and columns in your calculations.
Let G be a 2x2 matrix: G = [[a, b], [c, d]]. Show that G^T is equal to its matrix operation under commutation with respect to addition.
💡 Hint: Consider how transposing impacts each element's position.
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