12th Class Mathematics Determinants

  • question_answer 34)
    Write minors and cofactors of the following determinants:       (i)                        (ii)  

    Answer:

    (i)       Minor of element             = (1 ? 0) = 1       Minor of element 0 = M12 =       = (0 ?0) = 0       Minor of element 0 = M13 =       = (0 ? 0) = 0       Minor of element 0 = M21 =       = (0 ? 0) = 0       Minor of element 1 = M22 =       = (1 ? 0) = 1       Minor of element 0 = M23 =       = (0 ? 0) = 0       Minor of element 0 = M31 =       = (0 ? 0) = 0       Minor of element 0 = M32 =           = (0 ? 0) = 0       Minor of element 1 = M33 =              = (1 ? 0) = 1       Cofactor of element 1 = A11 = (?1)1+1M11             = (?1)2.1 = 1       Cofactor of element 0 = A12 = (?1)1+2 M12             = (?1)3. 0 = 0       Cofactor of element 0 = A13= (?1)1+3 M13             = (?1)4 .0 = 0       Cofactor of element 0 = A21= (?1)2+1 M21             = (?1)3 .0 = 0       Cofactor of element 1 = A22 = (?1)2+2 M22             = (?1)4 .1 = 1       Cofactor of element 0 = A23 = (?1)2+3 M23             = (?1)5 .0 = 0       Cofactor of element 0 = A31 = (?1)3+1 M31             = (?1)4 .0 = 0       Cofactor of element 0 = A32 = (?1)3+2 M32             = (?1)5 .0 = 0       Cofactor of element 1 = A33 = (?1)3+3 M33             = (?1)6 .1 = 1       (ii)         Minor of element             = (10 + 1) = 11       Minor of element 0 = M12 =             = (6 ? 0) = 6       Minor of element 4 = M13 =             = (3 ? 0) = 3       Minor of element 3 = M21 =             = (0 ? 4) = ?4       Minor of element 5 = M22 =             = (2 ? 2) = 2       Minor of element ? 1 = M23 =             = (2 ? 0) = 2       Minor of element ? 1 = M23 =             = (1 ? 0) = 1       Minor of element 0 = M31             = (0 ? 20) = ?20       Minor of element             = (?1 ? 12) = ?13       Minor of element 2 =             = (5 ? 0) = 5       Cofactor of element 1 = A11 = (?1)1+1 M11                     = (?1)2 . 11 = 11         Cofactor of element 0 = A12 = (?1)1+2 M12                     = (?1)3 .6 = ?6       Cofactor of element 4 = A13 = (?1)1+3 M13                     = (?1)4 . 3 = 3       Cofactor of element 3 = A21 = (?1)2+1 M21                     = (?1)3 . (?4) = 4       Cofactor of element 5 = A22 = (?1)2+2 M22                     = (?1)4 . 2 = 2       Cofactor of element ?1 = A23 = (?1)2+3 M23                   = (?1)5 . 1 = ?1       Cofactor of element 0 = A31 = (?1)3+1 M31                     = (?1)4 (?20) = ?20       Cofactor of element 1 = A32 = (?1)3+2 M32                     = (?1)5 . (?13) = 13       Cofactor of element 2 = A33 = (?1)3+3 M33                     = (?1)6 . 5 = 5  


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