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By using properties of determinants. Sho...

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`

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To show that \[ \begin{vmatrix} 1 + a^2 - b^2 & 2ab & -2b \\ 2ab & 1 - a^2 + b^2 & 2a \\ -2b & 2a & 1 - a^2 - b^2 \end{vmatrix} ...
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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

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: |(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)

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(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 that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

Using properties of determinant : Prove that |(a^(2), 2ab, b^(2)),(b^(2),a^(2),2ab),(2ab,b^(2),a^(2))| = (a^(3) + b^(3))^(2)

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

Using the properties of determinants, prove that following |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

NAGEEN PRAKASHAN ENGLISH-DETERMINANTS-Exercise 4.2
  1. Using the property of determinants and without expanding in questions ...

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  2. Using the property of determinants and without expanding in questions ...

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

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

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

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  8. By using properties of determinants. Show that:(i) |1a a^2 1bb^2 1cc^2...

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  9. Using the properties of determinants, show that: [[x, x^2, yz],[y, y...

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

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  11. By using properties of determinants. Show that:(i) |a-b-c2a2a2bb-c-a2b...

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  12. Using properties of determinants, prove the following: |1xx^2x^2 1...

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  13. By using properties of determinants. Show that:|1+a^2-b^2 2a b-2b2a b1...

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  14. Using properties of determinants, prove the following: |[a^2 + 1,ab, ...

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

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

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