Find the Cofactor Matrix [[5,2],[4,3]]

Problem

[[5,2],[4,3]]

Solution

1. Identify the matrix A and its elements (a_i*j)

A=[[5,2],[4,3]]

2. Calculate the minor (M_11) by removing the first row and first column, then find the cofactor (C_11)=(−1)(1+1)*(M_11)

(C_11)=(1)*(3)=3

3. Calculate the minor (M_12) by removing the first row and second column, then find the cofactor (C_12)=(−1)(1+2)*(M_12)

(C_12)=(−1)*(4)=−4

4. Calculate the minor (M_21) by removing the second row and first column, then find the cofactor (C_21)=(−1)(2+1)*(M_21)

(C_21)=(−1)*(2)=−2

5. Calculate the minor (M_22) by removing the second row and second column, then find the cofactor (C_22)=(−1)(2+2)*(M_22)

(C_22)=(1)*(5)=5

6. Assemble the cofactor matrix C using the calculated values (C_i*j)

C=[[3,−4],[−2,5]]

Final Answer

Cofactor Matrix=[[3,−4],[−2,5]]

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