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Cofactor

If A is a mat...

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If A is a matrix of order 3x3 and |a| = 2 then the determinant of cofactor matrix of A is

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Q. The value of the

m^{t h}

order determinant of a matrix

A

15

then the value of determinant formed by the cofactors of

A

if A is any square matrix of order 3x3 then |3A| is

A = [a_{i j}]

is a matrix of order

2 \times 2

, such that |A| = - 15 and

C_{i j}

represents the cofactor of

a_{i j}

a_{21} C_{21} + a_{22} C_{22} .

Q. Consider the matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 4 & 3 7 & 6 & 9 2 & 5 & 8 \end{matrix} ⎤ ⎥ ⎦ .

Then cofactor of element

9

A

Q. Assertion :Statement-1: Determinant of a skew-symmetric matrix of order 3 is zero. Reason: Statement-2: For any matrix A,

D e t (A) = D e t (A^{T})

D e t (- A) = - D e t (A)

D e t (A)

denotes the determinant of matrix A. Then,

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