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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that
`|{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^3`

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The correct Answer is:
`(a+b+c)^3`
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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1):}|=1+a^2+b^2+c^2

Using the property of determinants andd without expanding in following exercises 1 to 7 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

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,1,1),(a,b,c),(a^3,b^3,c^3):}|=(a-b)(b-c)(c-a)(a+b+c)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}|=2|{:(a,p,x),(b,q,y),(c,r,z):}|

KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. Solve system of linear equations , using matrix method if exists 2/x...

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  2. Solve system of linear equations , using matrix method if exists x-2...

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  3. Solve system of linear equations , using matrix method if exists 4x-...

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  4. Solve system of linear equations , using matrix method if exists x-y...

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  5. The sum of three numbrs is 6. If we multiply third number by 3 and add...

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  6. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

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  7. If anebnecand |{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}|=0 then p...

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  8. Prove that |{:(sqrt(13)+sqrt3,2sqrt5,sqrt5),(sqrt(15)+sqrt(26),5,sqrt(...

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  9. Prove that |{:(x^2,y^2,z^2),((x+1)^2,(y+1)^2,(z+1)^2),((x-1)^2,(y-1)^2...

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  10. Using the property of determinants andd without expanding in following...

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  11. Solve that |{:(1+x,1-x,1-x),(1-x,1+x,1-x),(1-x,1-x,1+x):}|=0

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  12. Show that |{:(sum(r=1)^(16)2^r,a,2(2^(16)-1)),(3sum(r=1)^(16)4^r,b,4(4...

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  13. If a1,a2,a3….ar are in G.P then show that |{:(a(r+1),a(r+5),a(r+9)),(a...

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  14. If pnea,qneb,rnec and |{:(p,b,c),(a,q,c),(a,b,r):}|=0 then prove that ...

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  15. A=[{:(-5,1,3),(7,1,-5),(1,-1,1):}]and B=[{:(1,1,2),(3,2,1),(2,1,3):}] ...

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  16. If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the val...

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  17. Solve |{:(4x,6x+2,8x+1),(6x+2,9x+3,12x),(8x+1,12x,16x+2):}|=0

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  18. If A+B+C=pi then find the value of |{:(sin^2A,sinAcosA,cos^2A),(sin^...

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  19. Prove that |{:(yz-x^2,zx-y^2,xz-z^2),(zx-y^2,xy-z^2,yz-x^2),(xy-z^2,...

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  20. Suppose three digit numbers A28 , 3B9 and 52C , where A,B and C are in...

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