Question

if A is also 2x2 matrix with 1st row [5-1] and 2nd row [ 2 2 ] the value of adjoint A is with​

Answer 1

Answer:

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Answer 2

Answer:

adjoint of A is    $\left[\begin{array}{cc}2&1\\-2&5\end{array}\right]$

Explanation:

given, the 2×2 matrix as:  $\left[\begin{array}{cc}5&-1\\2&2\end{array}\right]$

inorder to find adjoint of a matrix, first find the co- factors of the given matrix and then find the transpose of that co- factor matrix

cofactor of 5 is $C_{11}$ = $(-1)^{1+1}$ = 2

cofactor of -1 is $C_{12}$ = $(-1)^{1+2}$ = -2

cofactor of 2 is $C_{21}$ = $(-1)^{2+1}$ = 1

cofactor of 2 is $C_{22}$ = $(-1)^{2+2}$ = 5

cofactors of A =   $\left[\begin{array}{cc}2&-2\\1&5\end{array}\right]$

transpose of cofactors of matrix A =   $\left[\begin{array}{cc}2&1\\-2&5\end{array}\right]$

hence, adjoint of A =    $\left[\begin{array}{cc}2&1\\-2&5\end{array}\right]$