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Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 ...

Prove `|[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b, -2 a, 1-a^2-b^2]|=(1+a^2+b^2)^3`

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By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-2b],[2ab,1-a^2+b^2,2a],[2b ,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

Show that |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))|=(1+a^(2)+b^(2))^(3)

If A=[[1 , 2, 3],[ 2, 3 , 1]] and B=[[3, -1, 3],[ -1, 0, 2]] , then find 2 A-B .

If the derivative of the function f(x) is every where continuous and is given by f(x)={{:(bx^(2)+ax+4,,, x ge 1), (ax^(2)+b, ,, x lt -1):}, then : a)a = 2, b = -3 b)a = 3, b = 2 c)a = -2, b = -3 d)a = -3, b= -2

Prove that b^(2)c^(2) + c^(2)a^(2) + a^(2) b^(2) gt abc (a+b+c)

Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

If A = (1)/(3) [(1,2,2),(2,1,-2),(a,2,b)] is an orthogonal matrix, then a)a = - 2, b = - 1 b)a = 2, b = 1 c)a = 2, b = - 1 d)a = - 2, b = 1

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

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  2. Using properties of determinants prove the following. abs[[1,x,x^2...

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  3. Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b,...

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  4. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

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  5. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  6. Which of the following is correct? a)Determinant is a square matrix ...

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  7. Find the area of the triangle whose vertices are (3,8),(-4,2)and (5,1)

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  8. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  9. Find the area of the triangle with vertices at (1,0),(6,0),(4,3) using...

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  10. Using the property of determinants,show that the points A(a,b+c),B(b...

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  11. Find the values of k if area of triangle is 4 sq. units and vertices a...

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  12. Find the equation of line joining (1,2) and (3,6) using determinants.

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  13. If area of triangle is 35 sq. units with vertices (2,-6), (5,4) and (k...

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  14. Find the minor of 1 in the determinant Delta=|[3, 4, 5 ],[2, 7, 1]...

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  15. Find minors of element 6 in the determinant Delta=|[ 1, 2, 3],[ 4, ...

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  16. Find minors and cofactors of the elements of the determinant |[1 , -2]...

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  17. Find minors and cofactors of the elements a(11), a(21) in the determin...

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  18. Find minors and cofactors of the elements of the determinant |[2, -3,...

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  19. Write Minors and Cofactors of the elements of following determinants: ...

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  20. Using cofactors of element of second row evaluate Delta=|[5, 3, 8],[...

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