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ConceptElementary Transformations

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#### Question

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`

#### 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.

Using properties of determinants, prove that :

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

For what values of k, the system of linear equations

x + y + z = 2

2x + y – z = 3

3x + 2y + kz = 4

has a unique solution?

#### Reference Material

Solution for concept: Elementary Transformations. For the courses 12th CBSE (Arts), 12th CBSE (Commerce), 12th CBSE (Science), PUC Karnataka Science