1,019 prompts matching "A set closed under one operation but not another"
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Worked Example: The associative law for the product of three matrices
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Worked Example: Taking a common factor out of a matrix
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Explain Back: Why the order of the letters matters in a matrix product
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Explain Back: The rule that the transpose of a product reverses the order
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Worked Example: A singular matrix, and why it has no inverse
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Explain Back: The order of the answer when two matrices are multiplied
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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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Worked Example: What a determinant of nought means for a 2 by 2 matrix
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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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Worked Example: Evaluating a 3 by 3 determinant by the rule of Sarrus
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Worked Example: Forming the determinant Dy by replacing the second 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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Explain Back: Writing out the full matrix of cofactors
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Explain Back: Finding the adjoint of a 2 by 2 matrix quickly
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Worked Example: The identity that A times its adjoint gives the determinant times the identity
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Learn: Swapping and negating the entries when inverting a 2 by 2 matrix
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Learn: The order of the steps in inverting a 3 by 3 matrix
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