Using properties of determinants, pro...

Using properties of determinants, prove the following: `|1xx^2x^2 1xxx^2 1|=(1-x^3)^2`

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OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)

Using properties of determinants, prove the following: |1xx^2x^2 1...
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Using properties of determinants, prove the following: |1xx^2x^2 1...
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Prove that {:|(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab
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Prove that |{:(,1,a,a^(2)),(,1,b,b^(2)),(,1,c,c^(2)):}|=(a-b)(b-c)(c-a...
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Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(3)
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Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(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...
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Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2...
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Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)
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|[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc
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Using properties of determinants, prove that |a+x y z x a+y z x y a+z...
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Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2...
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Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...
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Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3
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Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y...
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Prove that: |(a^2+1, ab, ac),(ab, b^2+1, bc),(ac, bc, c^2+1)|=1+a^2+b^...
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Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,...
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Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,...
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IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)|=0, then using properties...
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Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(a+b+c)
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