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Using the property of determinants and without expanding, prove that:`|x a x+a y b y+b z c z+c|=0`

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Using the property of determinants and without expanding,prove that: det[[x,a,x+ay,b,y+bz,c,z+c]]=0

Using the property of determinants and without expanding, prove that: |b+c q+r y+z c+a r+p z+x a+b p+q x+y|=2|a p x b q y c r z|

Using the property of determinants and without expanding,prove that: det[[0,a,-b-a,0,-cb,c,0]]=0

Using the property of determinants and without expanding,prove that: det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

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

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Use the properties of determinant and without expanding prove that |{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}| = 2 |{:(a,p,x),(b,q,y),(c,r,z):}| .

Show without expanding at any stage that: [x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

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MODERN PUBLICATION-DETERMINANTS-NCERT FILE (Exercise 4.2)
  1. Using the property of determinants and without expanding, prove that:...

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  2. Using the property of determinants and without expanding, prove that:...

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  3. Using the property of determinants and without expanding, prove that |...

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  4. Using the property of determinants and without expanding, prove that:...

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  5. Use the properties of determinant and without expanding prove that |...

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  6. By using properties of determinants in |{:(0,a,-b),(-a,0,-c),(b,c,0):}...

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  7. Using properties of determinants, prove that |-a^2a b a c b a-b^2b cc...

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  8. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

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  9. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...

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  10. [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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  11. By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...

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  12. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

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  13. Prove that: |[a-b-c, 2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  14. Prove that Det[[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]]=2(x+y+z)^3

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  15. By using properties of determinants. Show that:|1xx^2x^2 1xxx^2 1|=(1-...

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  16. Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2...

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  17. Using properties of determinants, prove the following: |a^2a b a c...

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  18. Let A be a square matrix of order 3xx3, then |k A|is equal to(A) k|A|...

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  19. Which of the following is correct ?

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