05 3 x 3 Matrices

# 05 3 x 3 Matrices - 3 X 3 MATRICES THE IDENTITY MATRIX THE...

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3 X 3 M ATRICES : T HE I DENTITY M ATRIX , THE D ETERMINANT , AND THE I NVERSE For a three by three matrix, the identity matrix is = 1 0 0 0 1 0 0 0 1 I . It has the same properties as a two by two matrix, in that for a three by three matrix A, A IA AI + = . The determinant of a three by three matrix is defined in terms of the determinant of two by two submatrices: + - = f e c b g i h c b d i h f e a i h g f e d c b a To find the determinant of the 3 x 3 matrix, find the determinant of each of the 2 x 2 matrices. The matrices are composed of the elements in the first column multiplied by the 2 x 2 matrix formed by the four elements not in that column or row. Since a is in the first row and the first column, this is an even sum and a is positive. Since d is in the second row and the first column, this is an odd sum and d is negative. Lastly, since g is in the third row and the first column, this is an even sum and

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05 3 x 3 Matrices - 3 X 3 MATRICES THE IDENTITY MATRIX THE...

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