Question

show that all the diagonal elements of a skew symmetric matrix are zero

Answer 1

Answer:

See attachment

Step-by-step explanation:

Answer 2

Step-by-step explanation:

TO FIND: All the diagonal elements of a skew symmetric matrix are zero

skew symmetric matrix :

                                        A matrix can be skew symmetric only if it happens to be square. A skew-symmetric matrix is a matrix whose transposed form is equal to the negative of that matrix.

In case the transpose of a matrix happens to be equal to the negative of itself, then one can say that the matrix is skew symmetric. Therefore, for a matrix to be skew symmetric, A'=-A.

       Let us consider   $A=[a_{ij} ]$  is a skew symmetric matrix.

                       From definition $A^{T} =-A$

                          The    ( i j )  element of $A^{T}$ =The ( i j ) element of -A

                                    $a_{ij} =-a_{ji}$ , for al i and j

  For the diagonal elements  i=j , ( i i ) element of A = - ( i i ) element of A

                                     $a_{ij} =-a_{ii}$ , for all value of i.

                                     $2a_{ii} =0$

                                         $a_{ii} =0$ , for all values of i.

                    Therefore $a_{11} =a_{22}=a_{33} =a_{44}.............a_{nn} =0$                  

                                             

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