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Standard XII

Mathematics

Cofactor

The value of ...

Question

The value of the $m^{t h}$ order determinant of a matrix $A$ is $15$ then the value of determinant formed by the cofactors of $A$ will be

{(15)}^{m}

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15^{2 m}

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{(15)}^{m - 1}

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{(15)}^{2 m - 1}

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Solution

The correct option is C ${(15)}^{m - 1}$
If A be the matrix of order m and B is matrix of cofactors of a then determinant of B will be equal to ${(m - 1)}^{t h}$ power of the determinant of A.
$| B | = {| A |}^{m - 1}$
$∴ | B | = {(15)}^{m - 1}$

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Similar questions

Q. The value of a third order determinant is

11

, then the value of the square of the determinant formed by the cofactors will be

Q. Let

Δ_{o} =

⎡ ⎢ ⎣ \begin{matrix} a_{11} & a_{12} & a_{13} a_{21} & a_{22} & a_{23} a_{31} & a_{32} & a_{33} \end{matrix} ⎤ ⎥ ⎦

and let

Δ_{1}

denote the determinant formed by the cofactors of elements of

Δ_{0}

and

Δ_{2}

denote the determinant formed by the cofactor of

Δ_{1},

similarly

Δ_{n}

denotes the determinant formed by the cofactors of

Δ_{n - 1}

then the determinant value of

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Q. If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

If the determinant of a matrix of order $3 \times 3$ is formed by using the numbers 1 or -1 and minimum value of the determinant is $- λ$ , then the value of $λ$ is ___ .

Q. Let

Δ_{0} = ⎡ ⎢ ⎣ \begin{matrix} a_{11} & a_{12} & a_{13} a_{21} & a_{22} & a_{23} a_{31} & a_{32} & a_{33} \end{matrix} ⎤ ⎥ ⎦

(where

Δ_{0} \neq 0

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denote the determinant formed by the cofactors of elements of

Δ_{0}

and

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denote the determinant formed by the cofactor at

Δ_{1}

and so on

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The value of the mth order determinant of a matrix A is 15 then the value of determinant formed by the cofactors of A will be

The correct option is C (15)m−1If A be the matrix of order m and B is matrix of cofactors of a then determinant of B will be equal to (m−1)th power of the determinant of A.|B|=|A|m−1∴|B|=(15)m−1

The value of the $m^{t h}$ order determinant of a matrix $A$ is $15$ then the value of determinant formed by the cofactors of $A$ will be

The correct option is C ${(15)}^{m - 1}$
If A be the matrix of order m and B is matrix of cofactors of a then determinant of B will be equal to ${(m - 1)}^{t h}$ power of the determinant of A.
$| B | = {| A |}^{m - 1}$
$∴ | B | = {(15)}^{m - 1}$