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Show that the following systems of linear equations has infinite number of solutions and solve `x+2y=5,\ \ 3x+6y=15`

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To show that the system of linear equations has infinitely many solutions and to solve it, we will analyze the given equations step by step. ### Given Equations: 1. \( x + 2y = 5 \) (Equation 1) 2. \( 3x + 6y = 15 \) (Equation 2) ### Step 1: Check for Consistency We will first check if the two equations are consistent. To do this, we can manipulate Equation 2. ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Show that the following systems of linear equations are inconsisten...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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