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

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

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To show that the determinant \( |a \quad b \quad c \quad a+2x \quad b+2y \quad c+2z \quad x \quad y \quad z| = 0 \), we will perform row operations to simplify the determinant. ### Step-by-Step Solution: 1. **Write the Determinant**: \[ D = \begin{vmatrix} a & b & c \\ ...
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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

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

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

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

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

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

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

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

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

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

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  14. Find adjoint of the matrice in[(1,-1, 2),( 2, 3, 5),(-2, 0, 1)]

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  15. Verify A (a d j A) = (a d j A) A = |A|I for [(2 ,3),(-4,-6)]

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  16. Find adjoint of the matrice in[(1, 2),( 3, 4)]

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  17. Find the inverse the matrix (if it exists)given in[(-1, 5),(-3, 2)]

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  18. Find the inverse the matrix (if it exists)given in[(1, 2, 3),( 0, 2, 4...

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  19. Verify A (a d j A) = (a d j A) A = |A|I [(1,-1,2),(3,0,-2),(1,0,3)]

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

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