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Using properties of determinant prove th...

Using properties of determinant prove that `|a+b+c-c-b-c a+b+c-a-b-a a+b+c|=2(a+b)(b+c)(c+a)`

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Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

Prove that =|1 1 1 a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

Using the property of determinants and without expanding {:[( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)]:} =0

By using properties of determinants , show that : (i) {:[( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))]:}=(a-b)(b-c) (c-a) (ii) {:[( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))]:} =( a-b) (b-c)( c-a) (a+b+c)

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

Prove that |b+c a-b a c+a b-c b a+b c-a c|=3a b-a^3-b^3-c^3dot

Using the property of determinants and without expanding {:[( 1,bc,a(a+c) ),(1,ca,b( c+a)) ,( 1,ab,c(a+b) )]:}=0

CENGAGE-DETERMINANTS-All Questions
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  2. The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

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  3. Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a...

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  4. Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...

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  5. If omega!=1 is a cube root of unity and x+y+z!=0, then prove tha...

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  6. Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...

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  7. If A , Ba n dC are the angels of a triangle, show that |-1+cos B co...

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  8. If alpha,beta,gamma are the angles of a triangle and system of equatio...

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  9. Without expanding the determinants, prove that |103 115 114 111 108 10...

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  10. Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz ...

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  11. Find the value of determinant |(sqrt((13))+sqrt(3),2sqrt(5),sqrt(5))sq...

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  12. a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y...

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  13. Prove that the value of the determinant |-7 5+3i2/3-4i5-3i8 4+5i2/3+4i...

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  14. If the system of linear equation x+y+z=6,x+2y+3c=14 ,a n d2x+5y+lambda...

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  15. If ar=(cos2rpi+is in2rpi)^(1//9) , then prove that |a1a2a3a4a5a6a7a8a9...

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  16. Let f(x)=|2cos^2xsin2x-sinxsin2x2sin^2xcosxsinx-cosx0| . Then the val...

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  17. Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc...

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  18. The number of positive integral solutions of the equation |(x^3+1,x^2y...

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  19. If the value of determinant |(a,1,1),(1,b,1)(1,1,c)| is positive , the...

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  20. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x...

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