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Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[...

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

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Prove that: |[a+b, b+c, c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|

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Prove that: |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=|[a^2+1,b^2,c^2],[a^2,b^2+1,c^2],[a^2,b^2,c^2+1]|=1+a^2+b^2+c^2

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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]|

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

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  2. If A is a square matrix order 3 such that |adjA|=225, find |A'|.

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

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  4. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  5. Using Cofactors of elements of third column, evaluate triangle - |[1,x...

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  6. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  7. Find the inverse of the matrix A = {:[(a,b),(c,(1+bc)/a)] and show tha...

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  8. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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  9. If A = [[2,-3,5],[3,2,-4],[1,1,-2]] find A^-1. Using A^-1 solve the s...

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  10. Let P = [[3, -1, -2],[2 ,0 ,alpha ],[3, -5, 0]], where alpha in R. Sup...

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  11. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  12. Let M and n be two 3xx3 matrices such that MN = NM. Further, If Mne ...

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  13. For 3xx3 martrices M and N, which of the following statement (s) is ...

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  14. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

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  15. If A is a matrix of order mxx m such that A^(2) +A + 2I = O, then

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  16. Let a, b, and c be three real numbers satisfying [(a,b,c)][[1,9,7],[...

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  17. Let omega be a solution of z^3-1 = 0 If a = 2 , b=8 and c =7 then the ...

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  18. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  19. A complex number U = 4+2i.The value of |U| is

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  20. Let A be the set of all 3× 3 symmetric matrices all of whose either 0 ...

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