MATRIX ALGI BRA a ndo 2 10 100 E 010 001 Upper triangular matrix(Ek=0o 53 f) a ndo li 11 23 E=012 00 Lower triangular matrix(Ek=Oo 5b f) a ndo mle lb E 210 Matrix Manipulations Tudc, mt, rert c For two matrices, E and PoP is the transpose of E implies that xk= E a ndo mli 1l 123 456 n devrn Arr rert c dcr puFeuduert c For two matrices, E and Pomatrix addition and subtract ion are defined by E+P Er+ E-P=ER a ndo li 1h E 6 133 557° E-P 355MATRIX ALGEBRA 4 Example 10 A =    1 0 0 0 1 0 0 0 1    Upper triangular matrix (aik = 0, i > k) Example 11 A =    1 2 3 0 1 2 0 0 1    Lower triangular matrix (aik = 0, i < k) Example 12 A =    1 0 0 2 1 0 3 2 1    Matrix Manupulations Transposition For two matrices, A and B, B is the transpose of A implies that bik = aki Example 13 A =  1 2 3 4 5 6  , B = A′ =    1 4 2 5 3 6    Matrix Addition and Subtraction For two matrices, A and B, matrix addition and subtraction are defined by A + B = [aik + bik] A − B = [aik − bik] Example 14 A =  1 2 3 4 5 6  , B =  0 1 0 1 0 1  A + B =  1 3 3 5 5 7  , A − B =  1 1 3 3 5 5