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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online