Matrix and Determinant Formulas – HSC Math

Posted In: Mathematics
  1. Let A is a matrix with m row and n column. Then the dimension of a matrix A is m x n.
  2. Let A and B are matrices with dimension m x n and p x q respectively. Then multiplication of A and B, i.e. A.B is possible if and only if n=p.
  3. if $A=[\table a, b; c, d]$, then $A^{-1} = 1/{ad-bc}[\table d, -b; -c, a]$
  4. Given-
    $a_1x+b_1y+c_1y=d_1$ (1)
    $a_2x+b_2y+c_2y=d_2$ (2)
    $a_3x+b_3y+c_3y=d_2$ (3)

    Then,

    $$D = [\table a_1,b_1,c_1;a_2,b_2,c_2;a_3,b_3,c_3]$$
    $$D_x = [\table d_1,b_1,c_1;d_2,b_2,c_2;d_3,b_3,c_3]$$
    $$D_y = [\table a_1,d_1,c_1;a_2,d_2,c_2;a_3,d_3,c_3]$$
    $$D_z = [\table a_1,b_1,d_1;a_2,b_2,d_2;a_3,b_3,d_3]$$
    $$x = D_x/D$$
    $$y = D_y/D$$
    $$z = D_z/D$$


Post Tags: Algebra | HSC


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