Consider the matrix A- - 2 6 8 4 5 1 3 7 9 - The cofactor of element 5 in matrix A is-1 mark-

A= [ 2 amp; 6 amp; 8 4 amp; 5 amp; 1 3 amp; 7 amp; 9 ] Cofactor of element 5 is C_22=( 1)^2+2 2 amp; 8 3 amp; 9 ⇒ C_22=( 1)^4(18 24 ...

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Standard XII

Mathematics

Minor and Cofactor of a Matrix

Consider the ...

Question

Consider the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & 8 4 & 5 & 1 3 & 7 & 9 \end{matrix} ⎤ ⎥ ⎦ .$ The cofactor of element $5$ in matrix $A$ is

[1 mark]

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Solution

The correct option is B $- 6$
$A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & 8 4 & 5 & 1 3 & 7 & 9 \end{matrix} ⎤ ⎥ ⎦$
Cofactor of element $5$ is
$C_{22} = (- 1)^{2 + 2} ∣ ∣ ∣ \begin{matrix} 2 & 8 3 & 9 \end{matrix} ∣ ∣ ∣$
$\Rightarrow C_{22} = (- 1)^{4} (18 - 24)$
$\Rightarrow C_{22} = - 6$

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Similar questions

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[2 marks]

Q. The cofactor of element '5' in the matrix

⎛ ⎜ ⎝ \begin{matrix} 1 & - 3 & 2 4 & - 1 & 2 3 & 5 & 2 \end{matrix} ⎤ ⎥ ⎦

will be .

Q. Find cofactors of the elements of the matrix

A = [\begin{matrix} - 1 & 2 - 3 & 4 \end{matrix}]

In the matrix, write :
$A = ⎡ ⎢ ⎢ ⎣ \begin{matrix} 235 \sqrt{3} \end{matrix} \begin{matrix} 5 - 2 1 \end{matrix} \begin{matrix} 19 \frac{5}{2} - 5 \end{matrix} \begin{matrix} - 7 1217 \end{matrix} ⎤ ⎥ ⎥ ⎦$

(i) The order of the matrix
(ii) The number of elements
(iii) Write the elements $a_{13}, a_{21}, a_{33}, a_{24}, a_{23}$

Find the cofactor of the element $a_{32}$ in the matrix $⎡ ⎢ ⎣ \begin{matrix} 5 & 1 & 2 3 & 2 & 1 9 & 9 & 5 \end{matrix} ⎤ ⎥ ⎦$

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Consider the matrix A=⎡⎢⎣268451379⎤⎥⎦. The cofactor of element 5 in matrix A is [1 mark]

The correct option is B −6A=⎡⎢⎣268451379⎤⎥⎦ Cofactor of element 5 is C22=(−1)2+2∣∣∣2839∣∣∣ ⇒C22=(−1)4(18−24) ⇒C22=−6

Consider the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & 8 4 & 5 & 1 3 & 7 & 9 \end{matrix} ⎤ ⎥ ⎦ .$ The cofactor of element $5$ in matrix $A$ is

[1 mark]