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Show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]...

Show that `|[1+a,1,1],[1,1+b,1],[1,1,1+c]| = abc(1+1/a+1/b+1/c) = abc+bc+ca+ab`

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Show that Determinant of [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc (1+1/a+1/b+1/c)

Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(b)+(1)/(c))

By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .

By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^3,b^3,c^3]| = (a-b)(b-c)(c-a)(a+b+c)

Using the properties of determinants, show that |(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

If A= [[1,1,1],[1,1,1],[1,1,1]] then a. A^(3) = 9 A b. A^(3) = 27 A c. A + A = A^(2) d. A^(-1) does not exist

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]| = abc(1+1/a+1/b+1/c) = abc+b...

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  2. If A = [(13,-10),(7,87)], write the following submatrices of A. A12

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  3. If A = [(13,-10),(7,87)], write the following submatrices of A. A22

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  4. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  5. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  6. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  7. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  8. Find the minors and cofactos of each entry of the first column of the ...

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  9. Find the minors and cofactos of each entry of the first column of the ...

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  10. Find the minors and cofactos of each entry of the first column of the ...

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  11. Find the minors and cofactos of each entry of the first column of the ...

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  12. Evaluate the following determinants: {:|(-2,3),(4,-9)|

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  13. Evalate the following determinants: |(1//2, 8),(4,2)|

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  14. Evaluate the following determinants: |(a+ib , - c + id),(c+id, a-ib)...

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  15. Evaluate the following determinants: |(3x, x-7),(x+1,5x+1)|

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  16. Show that |(sin10^@, - cos10^@),(sin80^@, cos80^@)| = 1

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  17. Show that {:|(cos15^@, sin15^@),(sin75^@, cos75^@)|:}= 0

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  18. Evaluate |(x,x+1),(x-1,x)|

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  19. Evaluate the following determinants: |(1,0,0),(0,1,0),(0,0,1)|

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  20. Evaluate the following determinants: |(1,-3,3),(4,-1,3),(3,5,3)|

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  21. Evaluate the following determinants: |(1,0,2),(0,2,1),(2,0,3)|

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