1,246 prompts matching "Set theory laws: commutative and associative"
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Practice: A diagonal matrix
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Practice: The condition on the orders for a product to exist
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Learn: Deciding whether a stated matrix calculation is possible at all
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Practice: Evaluating AB minus BA
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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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Learn: The effect on a determinant of swapping two rows
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Practice: The sign pattern of the cofactors in a 3 by 3 determinant
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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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Learn: Solving two simultaneous equations by Cramer's rule
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Spot My Mistake: Checking a Cramer's rule solution by substituting back
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Practice: Turning a minor into a cofactor with the sign rule
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Spot My Mistake: Finding the adjoint of a 3 by 3 matrix
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Worked Example: The identity that A times its adjoint gives the determinant times the identity
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Quiz: Checking an inverse by multiplying to get the identity
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Practice: Why a 2 by 2 matrix with determinant nought cannot be inverted
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Learn: The order of the steps in inverting a 3 by 3 matrix
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Quiz: Checking a 3 by 3 inverse by multiplication
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