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midtermreview - -II o Inverse-III o Inverse-EA =-Express A...

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MATH 2J MIDTERM REVIEW SOLVING SYSTEM OF LINEAR EQUATIONS - Consistent vs. inconsistent - Strict triangular form o Back substitution - Elementary row operation o o o - Overdetermined system o equations __ unknowns o ____________ solution - Underdetermined system o equations __ unknowns o ____________ solutions - Gauss elimination Row Echelon Form: o o o - Gauss Jordan reduction Reduced R.E.F. o o MATRIX ALGEBRA - Addition, multiplication (condition, operation) - Matrix properties (ex. αβABCDEF) - Identity, diagonal, triangular, symmetric matrix ELEMENTARY MATRICES (E’s)
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Unformatted text preview: -II. o Inverse -III. o Inverse -EA = -Express A as product of E’s o E 4 E 3 E 2 E 1 A = I o A = o A-1 = -LU factorization: o Possible when: o E 3 E 2 E 1 A = o L = o Shortcut INVERSE-Definition:-To find A-1 : DETERMINANT (Notation: )-A invertable -A singular -det(I) = ; det(α) = -det(A: R i = 0) =-det(A: R i = R j ) = -Determinant & row operations: o o o-det(triangular matrix) = -det(A T ) =-det(A-1 ) =-det(AB) =-[2x2]-[3x3]-Find determinant of a matrix EIGEN VALUE/VECTOR; DIAGONALIZATION...
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