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Express the square of |{:(a1,b1,0),(a2,b...

Express the square of `|{:(a_1,b_1,0),(a_2,b_2,0),(a_3,b_3,0):}|` as a third order
determinant ,what is the value of this determinant ?

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The correct Answer is:
`|{:(a_1^2+b_1^2,a_1a_2+b_1b_2,a_1a_3+b_1b_3),(a_1a_2+b_1b_2,a_2^2+b_2^2,a_2a_3+b_2b_3),(a_3a_1+b_3b_1,a_2a_3+b_2b_3,a_3^2+b_3^2):}|;0`
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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , p...

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  2. Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}|, hence show that . |{:(0,c,b)...

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  3. Express the square of |{:(a1,b1,0),(a2,b2,0),(a3,b3,0):}| as a third o...

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  4. prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the va...

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  5. Prove that , the value of the determinant |{:(x+1,x+2,x+4),(x+3,x+5,...

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  6. |{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc

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  7. |{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2...

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  8. |{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...

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  9. |{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)

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  10. |{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3

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  11. |{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...

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  12. |{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...

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  13. |{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...

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  14. |{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0...

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  15. prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,...

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  16. If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+...

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  17. If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...

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  18. without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...

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  19. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

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  20. |{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0

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