Let An - -aij-n- n be a n - n determinant with the following conditionsaij -9 - i - j3- -i-j-10- other wise then

A_n = 9 amp; 3 amp; 0 amp; 0 amp; 0 amp; 0 amp; — nbsp; 3 amp; 9 amp; 3 amp; 0 amp; 0 amp; 0 amp; — nbsp; 0 amp; ...

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Properties of Determinants

Let An = [aij...

Question

Let $A_{n} = [a_{i j}]_{n \times n}$ be a $(n \times n)$ determinant with the following conditions
$a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 9, & i = j 3, & | i - j | = 1 0, & other wise \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$ then

A_{3} = 567

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A_{6} + 9 A_{4} = 9 A_{5}

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A_{6} + 9 A_{4} = 3 A_{5}

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A_{12} + 8 A_{10} = 81 A_{11}

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Solution

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Similar questions

A_{n} = [a_{i j}]_{n \times n}

(n \times n)

a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 9, & i = j 3, & | i - j | = 1 0, & other wise \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭

A = {[a_{i j}]}_{m \times n}

a_{i j} = 1

A (t) = [a_{i j}]

3 \times 3

a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 2 cos t, & if i = j 1, & if | i - j | = 1 0, & otherwise \end{matrix}

| A (t) |

A (t) .

A = a_{i j}

3,

a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x; & if i = j, x \in R 1; & if | i - j | = 1 0; & otherwise \end{matrix},

[a_{i j}]_{n \times n}

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