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Write the value of the following determinant `|(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|` |
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Answer» `|[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|` Applying `R_1->R_1+R_2+R_3` `=|[0,0,0],[b-c,c-a,a-b],[c-a,a-b,b-c]|` Here, all elements in first row are `0`. `:.` Value of the determinant is `0`. `=>|[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]| =0` |
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