Grade 12Algebra

I need to find the value of the attached determinant.

Question image for I need to find the value of the attached determina

Anupam Singh

8 Years agoGrade 12

2 Answers

gauri dixit

8 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 1^st and x from 2^nd determinant . in 2^nd one C1-> C1-C2, C2-> C2-C3. Then expand it result will be 0.

Now again split 1^st one by 2^nd row. Again you will get two determinants. Solve 2^nd one similarly as done above. Again result will be 0.For the 1^st 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)