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Show that |(x+2a,y+2b,z+2c),(x,y,z),(a,b...

Show that `|(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0.`

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Prove that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0

Show that |(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))|=(x-y)(y-z)(z-x)

Show that |(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3))|=xyz (x-y) (y-z) (z-x)

Show that |(x+y,y+z,z+x),(y+z,z+x,x+y),(z+x,x+y,y+z)|=2[3xyz-x^(3)-y^(3)-z^(3)]

If u=ax+by+cz , v=ay+bz+cx , w=ax+bx+cy , then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Solve that |(y+z,x,x^(2)),(z+x,y,y^(2)),(x+y,z,z^(2))|=(x+y+z)(x-y)(y-z)(z-x)

By using properties of determinants , show that : {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|= 2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

SURA PUBLICATION-MATRICES AND DETERMINANTS -EXERCISE 7.2
  1. Prove that |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)...

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  2. Prove that |(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc(1+(1)/(a)+(1)/(b)+(1)...

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  3. Prove that |(sec^(2)theta,tan^(2)theta,1),(tan^(2)theta,sec^(2)theta,-...

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  4. Show that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0.

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  5. Write the general form of a 3xx3 skew -symmetric matrix and prove that...

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  6. If |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0, prove that...

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  7. Prove that |(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)|= 0.

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  8. If a,b,c are p^(pt),q^(th) and r^(th) terms of an A.P., find the value...

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  9. Show that |(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2))...

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  10. If a,b,c are all positive, and are p^(th), q^(th) and r^(th) terms of ...

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  11. Find the value of |(1,log(x) y,log(x) z),(log(y) x,1,log(y) z),(log(z)...

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  12. If A = [((1)/(2),alpha),(0,(1)/(2))] , prove that sum(k=1)^(n)"det" (A...

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  13. Without expanding, evaluate the determinants : |(2,3,4),(5,6,8),(6x...

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  14. Without expanding evaluate the folleing determinents (ii)|(x+y,y+z,z+x...

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  15. If A is a square matrix and |A|=2, find the value of |"AA"|^(T) .

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  16. If A and B are square matrices of order 3 such that |A| = -1 and |B| =...

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  17. If lambda = -2, determine the value of |(0,2lambda,1),(lambda^(2),0,3l...

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  18. Determine the roots of the equation |(1,4,20),(1,-2,5),(1,2x,5x^(2))|=...

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  19. Verify that det (AB) = (det A) (det B) for A=[(4,3,-2),(1,0,7),(2,3...

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  20. Using cofactors of elements of second row, evaluate |A|, where A = [(5...

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