Lets define a 3 Times 3 matrix E its cofactor matrix C and i

Let\'s define a 3 Times 3 matrix, [E], its cofactor matrix, [C], and its Adjoint, [A]: [E] = 1 2 -1 2 5 -2 -1 2 2 ] [C] = Cof[E] [A]=Adj[E] Briefly, what is the relationship between [C] and [A]? That is, how do we convert [C] into [A]? Answer Here Rightarrow The [A] is the transpose of the [C] What are the cofactors of these elements? Cof(e_11) = 14 Cof(e_22) = 1 Now what are the cofactors of these elements? Cof(e_32) = 4 cof(e)23s) = 0 (1 pt ea) Define the Adjoint values for each of these elements: Adj(e_11) = Adj(e_22) = Adj(e_32) = Adj(e_32)

Solution

First we find the co-factor matrix C.Then the transpose of C is the adjoint matrix

Adjoint(A) = C^T ( transpose of C)

2) Cof(e11) = [ 5 2 , -2 2] = 10 -(-4) = (-1)^(1+1)14 = 14

Cof(e22) = [ 1 -1 , -1 2] = 2 -1 = (-1)^(2+2)*1 = 1

3) Cof(e32) = [ 1 -1 , 2 2] = 2- (-2) =(-1)^(3+2)*4 = -4

Cof(e23) = [1 2 , -1 -2] = -2 +2 =0

4) Transpose of C is the adjoint matrix

Adj(e11) = (-1)^(1+1)C11 = 14

Adj(e22) = (-1)^(2+2)*C22 = 1

Adj(e32) = (-1)^(3+2)C23 =0

Adj(e23) = (-1)^(2+3)*C32 =-4