1,252 prompts matching "Multi-part index exam question with a real context"
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Explain Back: Showing that AB and BA are usually different for 2 by 2 matrices
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Spot My Mistake: Squaring a 2 by 2 matrix
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Learn: The distributive law for a scalar over a sum of matrices
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Explain Back: Why the order of the letters matters in a matrix product
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Spot My Mistake: Orders that make a product possible one way round but not the other
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Quiz: Solving AX equals B and XA equals B by different routes
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Explain Back: The rule that the transpose of a product reverses the order
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Spot My Mistake: A symmetric matrix, equal to its own transpose
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Quiz: The zero matrix, and how it differs from nought in arithmetic
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Learn: Deciding whether a stated matrix calculation is possible at all
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Explain Back: Solving a matrix equation containing both a sum and a product
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Quiz: Finding an unknown entry from a stated matrix equation
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Learn: The effect on a determinant of swapping two rows
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Explain Back: The determinant of a product as the product of the determinants
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Quiz: Expanding a 3 by 3 determinant along a row or column containing noughts
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Spot My Mistake: Forming the determinant Dx by replacing the first column
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Learn: Solving two simultaneous equations by Cramer's rule
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Explain Back: What a coefficient determinant of nought says about the system
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Spot My Mistake: Checking a Cramer's rule solution by substituting back
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Quiz: Arranging the equations in standard form before applying Cramer's rule
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