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Show that the following systems of linear equations has infinite number of solutions and solve `x-y+3z=6,\ \ x+3y-3z=-4,\ \ 5x+3y+3z=10`

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To show that the given system of linear equations has an infinite number of solutions and to solve it, we will follow these steps: ### Given Equations: 1. \( x - y + 3z = 6 \) (Equation 1) 2. \( x + 3y - 3z = -4 \) (Equation 2) 3. \( 5x + 3y + 3z = 10 \) (Equation 3) ### Step 1: Write the system in matrix form ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Solve the following system of homogeneous equations: x+y+z=0 x-2y+z=0...

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  2. Show that the following systems of linear equations has infinite nu...

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  3. Show that the following systems of linear equations has infinite nu...

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  4. A salesman has the following record of sales during three months for t...

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  5. Solve the following system of equations 3x - 4y + 5z = 0, x + y - 2z =...

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  6. Solve the following system of homogeneous equations: x+y+z=0 x-2y+z=0...

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  7. Find the value of lambda for which the homogeneous system of equations...

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  8. If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y...

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  9. If a , b , c are distinct real numbers and the system of equations a x...

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  10. If x , y , z are not all zero such that a x+b y+c z=0 c x+a y+b z=0 ...

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  11. Solve following system of homogeneous linear equations: x+y-2z=0,\ ...

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  12. Solve following system of homogeneous linear equations: 2x+3y+4z=0,...

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  13. Solve following system of homogeneous linear equations: 3x+y+z=0,\ ...

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  14. Find the real values of lambda for which the following system of linea...

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  15. If a , b , c are non-zero real numbers and if the system of equations ...

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  16. If A is a singular matrix, then write the value of |A| .

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  17. For what value of x , the matrix [5-xx+1 2 4] is singular?

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  18. Write the value of the determinant |2 3 4 2x3x4x5 6 8| .

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  19. State whether the matrix [2 3 6 4] is singular or nonsingular.

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  20. Find the value of the determinant |4200 4201 4202 4203| .

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