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If A=[{:(2,5),(1,3):}] , find adj A....

If `A=[{:(2,5),(1,3):}]` , find adj `A`.

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To find the adjoint of the matrix \( A = \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix} \), we will follow these steps: ### Step 1: Find the Cofactor Matrix The cofactor matrix is obtained by calculating the cofactor for each element of the matrix \( A \). 1. **Cofactor of \( a_{11} = 2 \)**: - Minor of \( a_{11} \): The determinant of the matrix formed by removing the first row and first column, which is just \( 3 \). ...
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Knowledge Check

  • If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T) , then 5a+b is equal to

    A
    5
    B
    4
    C
    13
    D
    `-1`

  • If A=[{:(3,2),(1,4):}] then A. adj A is equal to :

    A
    `[{:(10,0),(0,10):}]`
    B
    `[{:(0,10),(10,0):}]`
    C
    `[{:(10,10),(0,0):}]`
    D
    `[{:(0,0),(10,10):}]`

  • If A=[{:(3,2),(1,4):}] , then what is A (adj A) equal to ?

    A
    `[{:(0,10),(10,0):}]`
    B
    `[{:(10,0),(0,10):}]`
    C
    `[{:(1,10),(10,1):}]`
    D
    `[{:(10,1),(1,10):}]`

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