1,332 prompts matching "Combining several index laws in one simplification"
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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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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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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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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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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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Learn: Swapping and negating the entries when inverting a 2 by 2 matrix
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Quiz: Checking an inverse by multiplying to get the identity
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Learn: The order of the steps in inverting a 3 by 3 matrix
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