Let a ij denote the element of the ith row and jth column in a 3 - 3 determinant 1- i- 3-1- j- 3 and let a ij - a ji for every i and j- Then the determinant has all the principal diagonal elements as

The correct option is A 0 i rowsj columnsIf ( i≤ i≤ 3,1≤ j≤ 3 ) then a _ ij =( a _ ji ) For principle diagonal elements i=j ⇒ a _ ii ...

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Standard XII

Mathematics

Skew Symmetric Matrix

Let a ij de...

Question

Let $a_{i j}$ denote the element of the $i^{t h}$ row and $j^{t h}$ column in a $3 \times 3$ determinant $(1 \leq i \leq 3, 1 \leq j \leq 3)$ and let $a_{i j} = - a_{j i}$ for every $i$ and $j$ . Then the determinant has all the principal diagonal elements as

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Solution

The correct option is A $0$
i-rows
j-columns
If $(i \leq i \leq 3, 1 \leq j \leq 3)$ then $a_{i j} = (- a_{j i})$
For principle diagonal elements
$i = j$
$\Rightarrow a_{i i} = - a_{i i} \Rightarrow 2 a_{i i} = 0$
$\Rightarrow a_{i i} = 0$
$∴$ The elements in principle diagonal are equal to $0$
Option C correct

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Let aij denote the element of the ith row and jth column in a 3×3 determinant (1≤i≤3,1≤j≤3) and let aij=−aji for every i and j. Then the determinant has all the principal diagonal elements as

The correct option is A 0i-rowsj-columnsIf (i≤i≤3,1≤j≤3) then aij=(−aji)For principle diagonal elementsi=j⇒aii=−aii⇒2aii=0⇒aii=0∴The elements in principle diagonal are equal to 0Option C correct

Let $a_{i j}$ denote the element of the $i^{t h}$ row and $j^{t h}$ column in a $3 \times 3$ determinant $(1 \leq i \leq 3, 1 \leq j \leq 3)$ and let $a_{i j} = - a_{j i}$ for every $i$ and $j$ . Then the determinant has all the principal diagonal elements as