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Show that |(b+c,bc,b^(2)c^(2)),(c+a,ca,c...

Show that `|(b+c,bc,b^(2)c^(2)),(c+a,ca,c^(2)a^(2)),(a+b,ab,a^(2)b^(2))|=0`.

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Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^(2)),(ab-c^(2),,bc-a^(2),,ca-b^(2)):}| |{:(a^(2),,c^(2),,2ca-b^(2)),(2ab-c^(2),,b^(2),,a^(2)),(b^(2),,2ac-a^(2),,c^(2)):}|.

If a,b and c are non- zero real number then prove that |{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0

Prove that |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))|=4a^(2)b^(2)c^(2).

Show that (a^(2)+b^(2),c^(2)),(b^(2)+c^(2),a^(2)) ,and (c^(2)+a^(2),b^(2)) are collinear

Prove that |(a,b),(c,d)|^(2)=|(a^(2)+c^(2),ab+cd),(ab+cd,b^(2)+d^(2))|

Show that |(b+c,a,a^(2)),(c+a,b,b^(2)),(a+b,c,c^(2))|=(a+b+c)(a-b)(b-c)(c-a)

Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) ]:} =4a^(2) b^(2) c^(2)

Show that |(0,a,c),(a,0,b),(c,b,0)|^(2)=|(2ac,ab,bc),(ab,-a^(2),-ac+b^(2)),(bc,-ac+b^(2),-c^(2))|

Prove that |(1/a^(2),bc,b+c),(1/b^(2),ca,c+a),(1/c^(2), ab, a+b)|=0

SURA PUBLICATION-MATRICES AND DETERMINANTS -EXERCISE 7.2
  1. Without expanding the determinant , prove that |(s,a^(2),b^(2)+c^(2)...

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  2. Show that |(b+c,bc,b^(2)c^(2)),(c+a,ca,c^(2)a^(2)),(a+b,ab,a^(2)b^(2))...

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  3. Prove that |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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