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Use suitable method(s) to evaluate the determinant of 1 2 0 32 2 5 1 1 1 0 1 2 1 2 2 4

 

Use suitable method(s) to evaluate the determinant of 1 2 0 32 2 5 1 1 1 0 1 2 1 2 2 4 -6 2 2 0 3 2 1 0 [Include stages of the calculation.] Let A = 3 x+y+z a+b+c ax + by + cz a +6 +c ax+by+cz x + y + ax + by + cz ax + by + c z Find det A as a product of linear factors. (It may help to factorise A as the product of two matrices and use the result which we will prove soon that det (BC) = det B det C.)

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