|{:(1," "1," "1),(1,1+x," "1),(1," "1,1+...

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

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

|{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xy+yz+zx+xyz

If |{:(x-1,1,1),(1,x+1,1),(-1,1,x+1):}|=0 , find the value of x.

Evaluate {:|(1,x,y),( 1,x+y,y),( 1,x,x+y)|:}

The x-coordinates of the vertices of a square of unit area are the roots of the equation x^2-3|x|+2=0 . The y-coordinates of the vertices are the roots of the equation y^2-3y+2=0. Then the possible vertices of the square is/are (a)(1,1),(2,1),(2,2),(1,2) (b)(-1,1),(-2,1),(-2,2),(-1,2) (c)(2,1),(1,-1),(1,2),(2,2) (d)(-2,1),(-1,-1),(-1,2),(-2,2)

If A={:[(1,2,x),(0,1,0),(0,0,1)]:}, B={:[(1,-2,y),(0,1,0),(0,0,1)]:} and AB=I_(3) , then find the value of x + y + 1.

Prove that, [[1+x,1,1],[1,1+y,1],[1,1,1+z]] = xyz(1 + 1/x+1/y+1/z)

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if |[x-1,1,1],[1,x+1,-1],[-1,1,x+1]| =0 , find the value of x.

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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2A

|{:(x,z,0),(0,y,y),(z,0,x):}|
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|{:(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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