|(x+y+z,-z,-y),(-z,x+y+z,-x),(-y,-x,x+y+...

`|(x+y+z,-z,-y),(-z,x+y+z,-x),(-y,-x,x+y+z)|=2(x+y)(y+z)(z+x)`

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Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

prove that: |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) What is the value of A(2, 3, 4)+B(2, 3, 4) ?

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) Whgat is the value D(1, 2, C(0, 1, 2)) ?

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) The value of C(1, 2, 3) is :

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) The value of D(0, 1, 2) is :

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))

Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=...
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For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...
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|(x+y+z,-z,-y),(-z,x+y+z,-x),(-y,-x,x+y+z)|=2(x+y)(y+z)(z+x)
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Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3
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|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|
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Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot
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Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...
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Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0
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Prove that |[x, sintheta, costheta],[-sintheta, -x, 1],[costheta, 1, ...
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Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/...
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Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2)...
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Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...
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|[(b+c)^2,ab,ca],[ab,(a+c)^2,bc],[ac,bc,(a+b)^2]|=2abc(a+b+c)^3
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Show that Delta=|(y+z)^2x y z xx y(x+z)^2y z x z y z(x+y)^2|=2x y z(x+...
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If a, b, c are positive and unequal, show that value of the determinan...
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Using properties of determinants, prove that |a a+b a+b+c2a3a+2b4a...
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Using properties of determinants. Prove that |1 1+p1+p+q2 3+2p4+3p+2q3...
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Q. |(x+y,x,x),(15x+4y,4x,2x),(10x +8y,8x,3x)|=x^3
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Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...
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Prove that |{:(a^(2), a^(2)-(b-c)^(2), bc), (b^(2), b^(2)-(c-a)^(2), ...
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