# Essay on Matrices

INDEX

adjoint.......................4, 5 algebraic multiplicity .....7 augmented matrix.........3 basis.........................3, 7 cofactor ........................4 coordinate vector ..........9 Cramer's rule................1 determinant...............2, 5 diagonal matrix .............6 diagonalizable...............8 dimension .....................6 dot product ...................8 eigenbasis ....................7 eigenspace...................7 eigenvalue ....................7 eigenvector...................7 geometric multiplicity....7 identity matrix ...............4 image ...........................6 inner product................9 inverse matrix...............5 inverse transformation..4

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To find x1 we replace the first column of A with vector y and divide the determinant of this new matrix by the determinant of A.

2 1 3 1 3 7 1 1 1 −8 x3 = = = −2 A 4

To find x3 we replace the third column of A with vector y and divide the determinant of this new matrix by the determinant of A.

Tom Penick

tomzap@eden.com

www.teicontrols.com/notes

2/29/2000 Page 1 of 10

THE DETERMINANT

The determinant of a matrix is a scalar value that is used in many matrix operations. The matrix must be square (equal number of columns and rows) to have a determinant. The notation for