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The value of |[[1,a,b+c],[1,b,c+a],[1,c,...

The value of `|[[1,a,b+c],[1,b,c+a],[1,c,a+b]]|` is

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

Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Using the property of determinants and without expanding , prove that: |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b]| = 0

Evaluate the following: {:|(1,a,b+c),(1,b,c+a),(1,c,a+b)|

If a, b and c are three vectors such that [a b c]=1, then find the value of [a+b b+c c+a]+[ atimesb btimesc ctimesa ]

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)

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

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

Evaluate |(1,a,a^2),(1,b,b^2),(1,c,c^2)|

Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Write the value of |(sin 10^@ - cos10^@),(sin 80^@ cos80^@)|

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  2. If A of order n xx n and det A = k, then find det (adj A).

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  3. The value of |[[1,a,b+c],[1,b,c+a],[1,c,a+b]]| is

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  4. If omega = (-1+sqrt3i)/2 , find the value of |(1, omega, omega^2),(ome...

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  5. Compute |(2,a,3),(4,b,6),(6,c,9)|

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  6. Find the area of the triangle whose vertices are (0,0),(a,0) and (0,b)

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  7. For what x, are the points (1,x), (2,2x), (3,3x) collinear?

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  8. Write down the adjoint of the matrix [(2,-1),(4,3)]

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  9. If A^-1 = [(0,1),(1,0)] and B^-1 = [(1,0),(0,1)], find (AB)^-1

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  10. Is the following system of equations consistent? 2x - 3y = 4, 3x + 2 y...

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  11. Find the number of solutions of the system of equations. 3x + 2y = 5, ...

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  12. If A is a scalar matrix of order 3xx3 such that a22 = 5, then find det...

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  13. If A is of order 5xx5 and det A = 1, find det (-A)

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  14. Find A^-1 if A = [(2,0),(0,3)]

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  15. If A = [(a,b),(c,d)], find adj (adj A)

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  16. If |A| = -5, find A (adj A).

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  17. Write the value of the determinant |(0,a-b,a-c), (b-a, 0, b-c),(c-a, c...

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  18. Find x if |(2x, 5),(3,x)| = |(16,5),(3,2)|

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  19. Without expanding, show that : Delta = {:|(cosec^2theta,cot^2theta,1...

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  20. Evaluate the following determinants: {:|(x^2-x+1,x-1),(x+1,x+1)|

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