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Write Minors and Cofactors of the elemen...

Write Minors and Cofactors of the elements of following determinants:
(i) `|(2,-4),( 0 ,3)|` (ii) `|(a ,c),( b, d)|`

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AI Generated Solution

To find the minors and cofactors of the elements of the given determinants, we will follow a systematic approach for both parts of the question. ### Part (i): Determinant `|(2, -4), (0, 3)|` 1. **Identify the elements of the determinant:** \[ \begin{vmatrix} 2 & -4 \\ ...
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Using properties of determinants. Prove that|(alpha,alpha^2,beta+gamma...

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  2. Evaluate |[1,x, y],[1,x+y, y],[1,x,x+y]|

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  3. Write Minors and Cofactors of the elements of following determinants:...

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  4. Using Cofactors of elements of second row, evaluate Delta=|(5, 3, 8),(...

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  5. Write Minors and Cofactors of the elements of following determinants:...

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  6. If Delta=|[a(11),a(12),a(13)],[a(21),a(22),a(23)],[a(31),a(32),a(33)]|...

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  7. Using Cofactors of elements of third column, evaluate Delta=|(1,x, y ...

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  8. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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  9. EvaluateDelta=|1a b c1b c a1c a b|

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  10. Show that |a b c a+2x b+2y c+2z x y z|=0

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  11. Prove that |a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3

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  12. Show that|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc(1+1/a+1/b+1/c)=abc+bc+ca+...

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  13. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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  14. Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

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  15. If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=...

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  16. Find the equation of the line joining A( 1,3) and B (0,0) using deter...

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  17. Find the minor of element 6 in the determinant Delta=|1 2 3 4 5 6 7 8 ...

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

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  19. Find the inverse the matrix (if it exists) given in[(2, 1, 3),( 4,-1, ...

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  20. If A=((2,-3,5),(3,2,-4),(1,1,-2)) find A^(-1). Use it to solve the sys...

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