# Solution - Elementary Transformations

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#### Question

Using properties of determinants, prove that :

|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc + bc + ca + ab

#### Solution

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Prove that  |(yz-x^2,zx-y^2,xy-z^2),(zx-y^2,xy-z^2,yz-x^2),(xy-z^2,yz-x^2,zx-y^2)|is divisible by (x + y + z) and hence find the quotient.

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Using the properties of determinants, solve the following for x:

|[x+2,x+6,x-1],[x+6,x-1,x+2],[x-1,x+2,x+6]|=0

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For what values of k, the system of linear equations

x + y + z = 2
2x + y – z = 3
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