696 prompts matching "Applying two index laws inside one expression"
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Explain Back: Why the order of the letters matters in a matrix product
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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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Worked Example: A singular matrix, and why it has no inverse
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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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Worked Example: What a determinant of nought means for a 2 by 2 matrix
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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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Worked Example: Evaluating a 3 by 3 determinant by the rule of Sarrus
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Spot My Mistake: Forming the determinant Dx by replacing the first column
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Worked Example: Forming the determinant Dy by replacing the second column
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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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Explain Back: Writing out the full matrix of cofactors
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Spot My Mistake: Checking cofactors by expanding the determinant along a second row
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Explain Back: Finding the adjoint of a 2 by 2 matrix quickly
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