If - -5 3 82 8 11 2 3- then minor of the element in 3rd row and 2nd column is-1 mark-

nbsp;Δ =5 amp;3 amp;8 2 amp;8 amp;1 1 amp;2 amp;3 Minor of the element in 3^rd row and 2^nd column =M_32 M_32=5 amp;8 2 amp;1 nbsp; ∴ M_32 ...

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Byju's Answer

Standard XII

Mathematics

Minor and Cofactor of a Matrix

If Δ =5 3 8...

Question

If $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 5 & 3 & 8 2 & 8 & 1 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣,$ then minor of the element in $3^{rd}$ row and $2^{nd}$ column is

[1 mark]

11

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Solution

The correct option is B $- 11$
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 5 & 3 & 8 2 & 8 & 1 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣$
Minor of the element in $3^{rd}$ row and $2^{nd}$ column $= M_{32}$
$M_{32} = ∣ ∣ ∣ \begin{matrix} 5 & 8 2 & 1 \end{matrix} ∣ ∣ ∣$
$∴ M_{32} = 5 - 16 = - 11$

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Similar questions

Consider the determinant

Δ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

M_{i j} =

Minor of the element of

i^{t h}

row &

j^{t h}

column.

C_{i j} =

Cofactor of element of

i^{t h}

row &

j^{t h}

column.

a_{3} M_{13} - b_{3} M_{23} + c_{3} M_{33}

is equal to

Consider the determinant

Δ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

M_{i j} =

Minor of the element of

i^{t h}

row &

j^{t h}

column.

C_{i j} =

Cofactor of element of

i^{t h}

row &

j^{t h}

column.

a_{2} . C_{12} + b_{2} . C_{22} + c_{2} . C_{32}

is equal to

Consider the determinant

Δ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

M_{i j} =

Minor of the element of

i^{t h}

row &

j^{t h}

column.

C_{i j} =

Cofactor of element of

i^{t h}

row &

j^{t h}

column.

Value of

b_{1} . C_{31} + b_{2} . C_{32} + b_{3} . C_{33}

Consider the determinant

Δ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

M_{i j} =

Minor of the element of

i^{t h}

row &

j^{t h}

column.

C_{i j} =

Cofactor of element of

i^{t h}

row &

j^{t h}

column.

If all the elements of the determinant are multiplied by 2, then the value of new determinant is

Q. Consider the determinant,

Δ = ∣ ∣ ∣ ∣ \begin{matrix} p & q & r x & y & z l & m & n \end{matrix} ∣ ∣ ∣ ∣

M_{0}

denotes the minor of an element in

i

th row and

j

th column and

C_{i j}

denotes the cofactor of an element in

i

th row and

j

th column.
The value of

p . C_{21} + q . C_{22} + r . C_{23}

is equal to

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If Δ=∣∣ ∣∣538281123∣∣ ∣∣, then minor of the element in 3rd row and 2nd column is [1 mark]

The correct option is B −11 Δ=∣∣ ∣∣538281123∣∣ ∣∣ Minor of the element in 3rd row and 2nd column =M32 M32=∣∣∣5821∣∣∣ ∴M32=5−16=−11

If $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 5 & 3 & 8 2 & 8 & 1 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣,$ then minor of the element in $3^{rd}$ row and $2^{nd}$ column is

[1 mark]

The correct option is B $- 11$
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 5 & 3 & 8 2 & 8 & 1 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣$
Minor of the element in $3^{rd}$ row and $2^{nd}$ column $= M_{32}$
$M_{32} = ∣ ∣ ∣ \begin{matrix} 5 & 8 2 & 1 \end{matrix} ∣ ∣ ∣$
$∴ M_{32} = 5 - 16 = - 11$