Given det [[a,b,c],[d,e,f],[g,h,i]] = -1, find the following determinants b) det [[a,b,c],[8a,8b,8c],[g,h,i]]  

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Given `det [[a,b,c],[d,e,f],[g,h,i]]=-1.`

We want to find the determinant of the matrix `[[a,b,c],[8a,8b,8c],[g,h,i]]` .

Now `det[[a,b,c],[8a,8b,8c],[g,h,i]]` `=8det[[a,b,c],[a,b,c],[g,h,i]]` by taking 8 outside.

Now we know that in the determinant if any row is a multiple of the other the value of the determinant is zero. Here we see that the first and...

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Given `det [[a,b,c],[d,e,f],[g,h,i]]=-1.`

We want to find the determinant of the matrix `[[a,b,c],[8a,8b,8c],[g,h,i]]` .

Now `det[[a,b,c],[8a,8b,8c],[g,h,i]]` `=8det[[a,b,c],[a,b,c],[g,h,i]]` by taking 8 outside.

Now we know that in the determinant if any row is a multiple of the other the value of the determinant is zero. Here we see that the first and the second row are equal.

Hence  `det[[a,b,c],[8a,8b,8c],[g,h,i]]=0`  .    Answer.

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