Question

When Triangularization method is is applied to x + y + z = 1 , 4x + 3y - z = 6; 3x + 5y + 3z = 4 Then the value L (lower triangular matrix is)
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Answer 1

Answer:

[1] x + y + z = 1   [2] 4x + 3y - z = 6   [3] 3x + 5y + 3z = 4 Solve by Substitution :

// Solve equation [1] for the variable  z 

 

[1] z = -x - y + 1

// Plug this in for variable  z  in equation [2]

  [2] 4x + 3y - (-x -y +1) = 6   [2] 5x + 4y = 7

// Plug this in for variable  z  in equation [3]

  [3] 3x + 5y + 3•(-x -y +1) = 4   [3] 2y = 1

// Solve equation [3] for the variable  y 

  [3] 2y = 1    [3] y = 1/2 

// Plug this in for variable  y  in equation [2]

  [2] 5x + 4•(1/2) = 7   [2] 5x = 5

// Solve equation [2] for the variable  x 

  [2] 5x = 5    [2] x = 1 

// By now we know this much :

  x = 1   y = 1/2   z = -x-y+1

// Use the  x  and  y  values to solve for  z 

  z = -(1)-(1/2)+1 = -1/2 

Solution :

 {x,y,z} = {1,1/2,-1/2} 

hope it helps you.

Answer 2

Answer:

A matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become the entries of the matrix. We use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs. When a system is written in this form, we call it an augmented matrix.

For example, consider the following 2 × 2system of equations.

3x + 4y = 7

4x − 2y = 5

We can write this system as an augmented matrix (please note that a more common formatting for augmented matrices has a solid vertical line running through the matrix, rather than a line on each row):

[34|74−2|5][34|74−2|5]

We can also write a matrix containing just the coefficients. This is called the

coefficient matrix.

[344−2][344−2]

A three-by-three system of equations such as

3x − y − z = 0

x + y = 5

2x − 3z = 2

has a coefficient matrix

⎡⎢⎣3−1−111020−3⎤⎥⎦[3−1−111020−3]

and is represented by the augmented matrix

⎡⎢⎣3−1−1∣0110∣5

How To

Given a system of equations, write an augmented matrix.

Write the coefficients of the x-terms as the numbers down the first column.

Write the coefficients of the y-terms as the numbers down the second column.

If there are z-terms, write the coefficients as the numbers down the third column.

Draw a vertical line and write the constants to the right of the line.

Step-by-step explanation:

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