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I need to find the value of the attached determinant.

I need to find the value of the attached determinant.

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Grade:12

2 Answers

gauri dixit
24 Points
6 years ago
hey Anupamam its answer is 0.Actually I couldn’t found how to attach image of solution .ok let me tell u steps you should follow
_if u have studied properties of determinants that a determinant can be expressed as the sum of two determinant\begin{vmatrix} a^{3} -x&a^{4}-x &a^{5}-x \\ a^{5}-x& a^{6}-x &a^{7}-x\\ a^{7}-x &a^{8-}x &a^{9}-x \end{vmatrix} =\begin{bmatrix} a^{3}&a^{4} &a5 \\ a^{5}-x&a^{6}-x &a^{7}-x \\ a^{7}-x &a^{8}-x &a^{9}-x \end{bmatrix}  – \begin{vmatrix} x &x &x \\ a^{5}-x&a^{6}-x &a^{7}-x \\ a^{7}-x&a^{8}-x &a^{9}-x \end{vmatrix}
 
now take a3 common from 1st and x from 2nd determinant . in 2nd one C1-> C1-C2, C2-> C2-C3. Then expand it result will be 0.
Now again split 1st one by 2nd row. Again you will get two determinants. Solve 2nd one similarly as done above. Again result will be 0.For the 1st part it will now look liike
a^{3}\begin{vmatrix} 1& a& a^{2}\\ a^{5} &a^{6} &a^{7} \\ a^{7}-x&a^{8}-x &a^{9}-x \end{vmatrix}
Now take a5 common from row two. You will find that Row 1 and Row 2 will become same .Then you know by properties result will be zero.(plz ignore typing mistakes)
Snehith
13 Points
6 years ago
Yes it is zero. You can easily find it by applying determinant properties. step 1 r o w 1 becomes r o w 1 - r o w 2 proceed like this..thanks

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