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By using properties of determinants. Sho...

By using properties of determinants. 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`

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|{:(" "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

The value of the determinant |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))| is equal to

Using the properties of determinants, prove that following |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

By using properties of determinants , show that : (i) {:|( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))|:}=(a-b)(b-c) (c-a) (ii) {:|( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))|:} =( a-b) (b-c)( c-a) (a+b+c)

Using properties of determinants prove that, |{:((b+c)^(2),a^(2),a^(2)),(b^(2),(c+a)^(2),b^(2)),(c^(2),c^(2),(a+b)^(2)):}|=2abc(a+b+c)^(3)

Using formula let's show that. (3a-4b)^2 + 24ab = 9a^2 +16b^2

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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)) |:}

prove that , |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|=-(a^3+b^3)^2

Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2 .

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  2. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

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  3. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  4. Which of the following values of alpha satisfying the equation |(1+alp...

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  5. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

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  6. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

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  7. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

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  8. The value of |y z z xx y p2p3r1 1 1|,w h e r ex ,y ,z are respectively...

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  9. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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  10. Prove that the value of each the following determinants is zero: |s...

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  11. The number of values of k for which the system of the equations (k+1)x...

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  12. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

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  13. " if " |{:(a^(2),,b^(2),,c^(2)),((a+1)^(2),,(b+1)^(2),,(c+1)^(2)),((a-...

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  14. Statement 1: "Delta"= |[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m ...

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  15. Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]|=2(a-b)(b...

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  16. If =|sin theta cos var phi sin theta sin var phi cos theta cos theta c...

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  17. The system of equations -2x+y+z=a, x-2y+z=b, x+y-2z=c, has: (a)no so...

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  18. Show that if x1, x2, x3!=0 abs((x1+a1.b1,a1.b2,a1.b3),(a2.b1,x2+a2.b...

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  19. If determinant |[cos(theta+phi),-sin(theta+phi),cos2phi],[sin theta,co...

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  20. If Deltar =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1,...

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