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Prove that: {:|(b+c,a-b,a),(c+a,b-c,b)...

Prove that:
`{:|(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)|=3abc -a^3-b^3-c^3`

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Prove that |[b+c,a,a],[b,c+a,b],[c,c,a+b]| = 4abc

Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b+c)^3

Without expanding, prove the following |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^3+b^3+c^3-3abc

Prove that: |{:(-2a, a+b, a+c), (b+a,-2b,b+c),(c+a, c+b,-2c):}|=4(a+b)(b+c)(c+a)

Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

Without expanding, prove the following |(a,b-c,c-b),(a-c,b,c-a),(a-b,b-a,c)|=(a+b-c)(b+c-a)(c+a-b)

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: {:|(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)|=3abc -a^3-b^3-c^...

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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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