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Level 340

Inverse of a Matrix


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invertible matrix
a square matrix that possesses an inverse
Inverse
a + (-a) = 0 = (-a) + a OR a * 1/a = 1 = 1/a * a; a cant be 0
singular matrix
a matrix that has no inverse
nonsingular matrix
an invertible matrix
elementary matrix
an invertible matrix that results by performing one elementary row operation on an identity matrix
determinant
ad-bc; must be nonzero for an invertible matrix
algorithm for finding inverse
row reduce the augmented matrix [A I]. If A is row equivalent to I, then [A I] is row equivalent to [I A^-1] (otherwise, A doesn't have an inverse)
AB = I
If _______________, A and B are both invertible and inverses of each other
invertible linear transformation T
there exists a function S: R^n -> R^n such that S (T(x)) = x for all x in R^n and T(S(x))=x for all x in R^n
inverse of transformation T
S such that T is invertible
Conditions for inverse
in an mxn Matrix A
Inverse => L.I. ?
every column is L.I. - all pivot column