If matrix D₁= diag (a, b, c) , matrix D₂= diag (3,3,3) and A is a skew symmetric matrix of 3^ rd order, then Tr (D₁ D₂ A+D₁ D₂+D₁ A+D₂ A )- Tr (D₁+D₂ )=

Step-by-step solution

A is skew symmetric matrix of 3^ rd order aligned & diag ( A )=(0,0,0) & diag ( D ₁ D ₂ ~A + D ₁ D ₂+ D ₁ ~A + D ₂ ~A )- dia ( D ₁+ D ₂ ) & = diag (a 3 0+a 3+a 0+3 0, b 3 0+b & 3+b 0+3 0, c 3 0+c 3+c 0+3 0) & - diag (3+a, b+3) & = diag (3 a, 3 b, 3 c)- diag (3+a, b+3) & = diag (2 a-3,2 b-3,2 c-3) & Now, Tr ( D ₁ D ₂ ~A + D ₁ D ₂+ D ₁ ~A + D ₂ ~A )- Tr ( D ₁+ D ₂ ) & =2 a-3+2 b-3+2 c-3=2 a+2 b+2 c-9 aligned