If |(a,b,aalpha+b),(b,c,balpha+c),(aalph...

If `|(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0,` prove that a,b,c, are in G.P. or `alpha` is a root of `ax^(2)+`2bx+c=0

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If |{:(a,b,a alpha+b),(b,c,b alpha+c),(a alpha +b,b alpha+c,0):}|=0 Prove that a,b,c are in G.P. or alpha is a root of ax^2 + 2bx + c=0

If a , b, c, … are in G.P. then 2a,2b,2c,… are in ….

In the quadratic ax^2+bx+c=0,D=b^2-4ac and alpha+beta,alpha^2+beta^2,alpha^3+beta^3, are in G.P , where alpha,beta are the roots of ax^2+bx+c, then (a) Delta != 0 (b) bDelta = 0 (c) cDelta = 0 (d) Delta = 0

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If |(a,b-c,b+c),(a+c,b,c-a),(a-b,a+b,c)|=0 then the line ax+by+c=0 passes through the fixed point which is

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If alpha" and "beta, alpha" and "gamma" and "alpha" and "delta are the roots of the equations ax^(2)+2bx+c=0, 2bx^(2)+cx+a=0" and "cx^(2)+ax+2b=0 respectively, where a,b and c are positive real numbers, then alpha+alpha^(2)=

SURA PUBLICATION-MATRICES AND DETERMINANTS -EXERCISE 7.2

Prove that |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)...
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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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Prove that |(sec^(2)theta,tan^(2)theta,1),(tan^(2)theta,sec^(2)theta,-...
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Show that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0.
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Write the general form of a 3xx3 skew -symmetric matrix and prove that...
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If |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0, prove that...
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Prove that |(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)|= 0.
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If a,b,c are p^(pt),q^(th) and r^(th) terms of an A.P., find the value...
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Show that |(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2))...
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If a,b,c are all positive, and are p^(th), q^(th) and r^(th) terms of ...
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Find the value of |(1,log(x) y,log(x) z),(log(y) x,1,log(y) z),(log(z)...
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If A = [((1)/(2),alpha),(0,(1)/(2))] , prove that sum(k=1)^(n)"det" (A...
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Without expanding, evaluate the determinants : |(2,3,4),(5,6,8),(6x...
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Without expanding evaluate the folleing determinents (ii)|(x+y,y+z,z+x...
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If A is a square matrix and |A|=2, find the value of |"AA"|^(T) .
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If A and B are square matrices of order 3 such that |A| = -1 and |B| =...
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If lambda = -2, determine the value of |(0,2lambda,1),(lambda^(2),0,3l...
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Determine the roots of the equation |(1,4,20),(1,-2,5),(1,2x,5x^(2))|=...
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Verify that det (AB) = (det A) (det B) for A=[(4,3,-2),(1,0,7),(2,3...
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Using cofactors of elements of second row, evaluate |A|, where A = [(5...
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