Matrix Inverse, the Determinant, and Matrix Equations (VCE SSCE General Mathematics): Flashcards
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Notation for inverse of matrix
Notation for inverse of matrix
Result of
Result of
Identity matrix
Matrix with 1s on diagonal, 0s elsewhere
Matrix with 1s on diagonal, 0s elsewhere
Identity matrix
Formula:
Formula:
Condition for matrix to have inverse
Condition for matrix to have inverse
Determinant must be non-zero
Matrix with determinant = 0
Matrix with determinant = 0
Singular matrix (no inverse)
Steps to find 2×2 inverse
Steps to find 2×2 inverse
Swap diagonal, negate off-diagonal, divide by det
Matrix multiplication commutativity
Matrix multiplication commutativity
Not commutative:
Pre-multiply by inverse when is where
Pre-multiply by inverse when is where
On the right side
Post-multiply by inverse when is where
Post-multiply by inverse when is where
On the left side