|{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}...

`|{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(x-4)^2`

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By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordered pair (A,B) is equal to

By using properties of determinants , show that : (i) {:|( x+4, 2x, 2x),( 2x,x+4, 2x),( 2x,2x, x+4) |:}=( 5x +4) (4-x)^(2) ( ii) {:|( y+k , y , y ),( y,y+ k , y ),( y,y , y+k ) |:} =k^(2) ( 3y +k )

|{:(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x):}|=x^3

Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

|{:(x," "4,-2),(4," "x,-2),(4,-2," "x):}|=0

|{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64):}|=0

If |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)|=0 , then the value of x is -

If a,b,c are in A.P. then the determinant {:|( x+2,x+3,x+2a),( x+3,x+4,x+2b),( x+4,x+5,x+2c)|:} is

Find values of x, if (i) {:|( 2,4),(5,1)|:}={:|( 2x,4),(6,x) |:}" "(ii) {:|( 2,3),(4,5)|:}={:|( x,3),( 2x,5)|:}

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

|{:(a,b,c),(a^2,b^2,c^2),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)
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|{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xy+yz+zx+xyz
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|{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(x-4)^2
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|{:(1+a,1,1),(1,1+a,1),(1,1,1+a):}|=a^3+3a^2
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|{:(1,b+c,b^2+c^2),(1,c+a,c^2+a^2),(1,a+b,a^2+b^2):}|=(b-c)(c-a)(a-b)
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|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|=?
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|{:(-1,b,c),(a,-1,c),(a,b,-1):}|=(a+1)(b+1)(c+1)((a)/(a+1)+(b)/(b+1)+(...
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|{:(x^2+y^2+1,x^2+2y^2+3,x^2+3y^2+4),(y^2+2,2y^2+6,3y^2+8),(y^2+1,2y^2...
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|{:(" "3a," "-a+b,-a+c),(a-b," "3b," "c-b),(a-c," "b-c," "3c):}|...
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|{:(x,a,b),(a,x,b),(a,b,x):}|=(x-a)(x-b)(x+a+b)
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|{:(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c):}|=3abc-a^3-b^3-c^3
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Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c...
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|{:(a^2,a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b)^2,ab):}|=(...
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|{:((a+1)(a+2),a+2,1),((a+2)(a+3),a+3,1),((a+3)(a+4),a+4,1):}|=-2
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Show that the following determinant is a perfact square : |{:(1,a,a^...
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if x+y+z = 0 then prove that |{:(x,y,z),(x^2,y^2,z^2),(y+z,z+x,x+y):}|...
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|{:(1,1,1),(x,y,z),(x^3,y^3,z^3):}|=0
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|{:(x," "4,-2),(4," "x,-2),(4,-2," "x):}|=0
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|{:(x,a,a),(a,x,b),(b,b,x):}|=0
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|{:(x+1," "2," "3),(" "1,x+1," "3),(" "3,-6,x+1):}|=0
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