|{:(" "1," "z,-y),(-z," "1," "x),(" "y,-...

`|{:(" "1," "z,-y),(-z," "1," "x),(" "y,-x," "1):}|`

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The correct Answer is:

`x^2+y^2+z^2+1`

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Without expanding prove that Delta ={:|( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) |:} =0

if x+y+z=0 , then show that, |{:(1,1,1),(x,y,z),(x^3,y^3,z^3):}|=0

If a x_1^2+b y_1^2+c z_1^2=a x_2 ^2+b y_2 ^2+c z_2 ^2=a x_3 ^2+b y_3 ^2+c z_3 ^2=d ,a x_2 x_3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f, then prove that |(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3,y_3,z_3)|=(d-f){((d+2f))/(a b c)}^(1//2)

If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , prove that, xyz=-1.

Using properties of determinants porve that, |{:(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3):}|=(1+pxyz)(x-y)(y-z)(z-x)

{:|( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) |:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

For any scalar c prove that, |{:(x,x^2,1+cx^3),(y,y^2,1+cy^3),(z,z^2,1+cz^3):}|=(1+cxyz)(x-y)(y-z)(z-x)

If x,y,z are different and Delta = {:|( x,x^(2) , 1+x^(3)),( y,y^(3) ,1+y^(3)),( z,z^(3) ,1+z^(3)) |:} then value of delta?

tan^(-1)""(x-y)/(1+xy)+tan^(-1)""(y-z)/(1+yz)+tan^(-1)""(z-x)/(1+zx) =tan^(-1)""(x^(2)-y^(2))/(1+x^(2)y^(2))+tan^(-1)""(y^(2)-z^(2))/(1+y^(2)z^(2))+tan^(-1) ""(z^(2)-x^(2))/(1+z^(2)x^(2))

Solve for x, y and z, if {:((x+y,2),(1,0))={:((2,x-z),(2x-y,0)):}

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2A

|{:(1,a,bc),(1,b,ca),(1,c,ab):}|
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|{:(1," "1," "1),(1,1+x," "1),(1," "1,1+y):}|
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|{:(1+a," "b," "c),(" "a,1+b," "c),(" "a," "b,1+c):}|
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|{:(" "1," "z,-y),(-z," "1," "x),(" "y,-x," "1):}|
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|{:(-a," "a," "a),(" "b,-b," "b),(" "c," "c,-c):}|
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|{:(0," "sinalpha,-cosbeta),(cosalpha," "0," "sinbeta),(cos alpha,-sin...
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write minor and cofactor ; |{:(5,2),(0,-1):}|
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write minor and cofactor ; |{:(-1,4),(2,3):}|
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write down the minor and cofactor |{:(1,a,bc),(1,b,ca),(1,c,ab):}|
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write down the minor and cofactor |{:(0,2,6),(1,5,0),(3,7,1):}|
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Evaluate the determinant |{:(" "2,3,-5),(" "7,1,-2),(-3,4," "1):}| ...
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If [.] denotes the greatest ingeter less then or equal to the real num...
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Evalute the determinant D=|{:(" "1," "sintheta,1),(-sintheta," "1,si...
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Find the minors and the cofactors of each element of the first column ...
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If A=[{:(1,3),(2,1):}],find the determinant of the matrix A^2-2A.
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If A =[{:(1,0,1),(0,1,2),(0,0,4):}], then show that |3A|=27|A|.
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If A = [{:(2,5),(2,1):}] and B =[{:(4,-3),(2,5):}] ,verify that |AB|...
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If f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasinthe...
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Find the integral value of x if |{:(x^2,x,1),(0,2,1),(3,1,4):}|=28
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prove that : |{:(1,a,b),(-a,1,c),(-b,-c,1):}|=1+a^2+b^2+c^2
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