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By using properties of determinants. Sho...

By using properties of determinants. Show that:`|[1+a^2-b^2, 2a b,-2b],[2a b,1-a^2+b^2, 2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3`

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Given `|[1+a^2-b^2, 2a b,-2b],[2a b,1-a^2+b^2, 2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3`
Solving LHS
`|[1+a^2-b^2, 2a b,-2b],[2a b,1-a^2+b^2, 2a],[2b,-2a,1-a^2-b^2]|`
applying `R_1->R_1+bR_3`
...
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By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3

By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3

Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3

Using properties of determinants, prove that: |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))|=(1+a^(2)+b^(2))^(3)

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2b,,-2a,,1-a^(2)-b^(2)):}| = (1+a^(2) +b^(2))^(3)

Using properties of determinants, show that |1 a a^2 -b c 1 b b^2 -c a 1 c c^2 -a b|=0

Using properties of determinants, prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]|=a^3

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)

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

NCERT ENGLISH-DETERMINANTS-All Questions
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  3. Use product [1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2] to solve th...

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  4. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

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

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  7. By using properties of determinants. Show that:|[1,x,x^2],[x^2, 1,x],[...

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  8. By using properties of determinants. Show that:|[1+a^2-b^2, 2a b,-2b],...

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  9. By using properties of determinants. Show that:|[a^2+1,a b, a c],[ a b...

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

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  11. Which of the following is correct (A)   Determinant is a square matrix...

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  12. Solve system of linear equations, using matrix method, 4x - 3y = 3" "...

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  13. Solve system of linear equations, using matrix method, 2x - y = -2" "...

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  14. Examine the consistency of the system of equations x + 3 y = 5" "2x + ...

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  15. Examine the consistency of the system of equations 2x - y = 5" "x + y ...

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  16. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost o...

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  18. Find the inverse the matrix (if it exists)given in[(1,-1, 2),( 0, 2,-3...

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  19. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  20. If A=[(3, 1),( 1, 2)], show that A^2-5A+5I=0. Hence, find A^(-1).

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