Manipulating Determinants (AQA A-Level Further Maths): Flashcards
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10 cards from this deck
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Practise the cards
10 cards from this deck
Flexibility in calculating 3×3 determinants
Flexibility in calculating 3×3 determinants
Can use any row or any column
Sign pattern for expanding determinants (top-left corner)
Sign pattern for expanding determinants (top-left corner)
Starts with + in checkerboard pattern
Relationship between and
Relationship between and
Operation that preserves determinant value
Operation that preserves determinant value
Add/subtract multiple of row/column to another row/column
Effect of swapping two rows on determinant
Effect of swapping two rows on determinant
Changes sign:
Effect of multiplying row by scalar on determinant
Effect of multiplying row by scalar on determinant
Multiplies determinant by
Best strategy before expanding a determinant
Best strategy before expanding a determinant
Create zeros using row/column operations
Effect of even number of row swaps on determinant sign
Effect of even number of row swaps on determinant sign
Signs cancel out, determinant remains positive
Condition for system of equations to have unique solution
Condition for system of equations to have unique solution
Determinant must be non-zero
Two operations that change determinant sign
Two operations that change determinant sign
Swapping two rows OR swapping two columns