In a third order determinant aij denotes the element in the ith row and the jth column If aij - 0- i - j 1- i - j -1- i - j- then the value of the determinant

The correct option is A 0 a_ij = #160;{0, amp; i = j 1, amp; i gt; j 1, #160; amp; i lt; j. #160;Let A=[ 0 amp; ...

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Standard XII

Mathematics

Determinant

In a third or...

Question

In a third order determinant $a_{i j}$ denotes the element in the ith row and the jth column If $a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 0, & i = j 1, & i > j - 1, & i < j \end{matrix}$ then the value of the determinant

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Solution

The correct option is A 0
$a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 0, & i = j 1, & i > j - 1, & i < j \end{matrix}$

Let $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & - 1 & - 1 1 & 0 & - 1 1 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦$

Now, $| A | = ∣ ∣ ∣ ∣ \begin{matrix} 0 & - 1 & - 1 1 & 0 & - 1 1 & 1 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$= 1 - 1 = 0$

$\Rightarrow | A | = 0$

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Similar questions

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In a third order determinant aij denotes the element in the ith row and the jth column If aij=⎧⎪⎨⎪⎩0,i=j1,i>j−1,i<j then the value of the determinant

The correct option is A 0aij=⎧⎪⎨⎪⎩0,i=j1,i>j−1,i<j Let A=⎡⎢⎣0−1−110−1110⎤⎥⎦Now, |A|=∣∣ ∣∣0−1−110−1110∣∣ ∣∣ =1−1=0⇒|A|=0

In a third order determinant $a_{i j}$ denotes the element in the ith row and the jth column If $a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 0, & i = j 1, & i > j - 1, & i < j \end{matrix}$ then the value of the determinant