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

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masterpiece11 | Student | (Level 1) Salutatorian

Posted April 28, 2013 at 1:02 AM via web

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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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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted April 28, 2013 at 10:58 AM (Answer #1)

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If rows of a matrix are linearly dependent then its determinant is 0.

Rows of this matrix are obviously dependent because

`8cdot[a,b,c]=[8a,8b,8c]`

Hence

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

 

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