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AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

Section: Mathematics

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Question : 6 of 160

Marks: +1, -0

The solution of the linear system of equations

\begin{bmatrix} 2 & 2 & 3 \\ 7 & 1 & 1 \\ 0 & 6 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 3y+11 \\ 6z-1 \\ 5y+11 \end{bmatrix} + \begin{bmatrix} x \\ x \\ 4z \end{bmatrix} + \begin{bmatrix} z \\ 3x \\ 4y \end{bmatrix}

is

x = 4 , y = - 3 , z = 2
x = 2 , y = 1 , z = 1
x = 1 , y = - 1 , z = 2
x = 2 , y = - 4 , z = 3

Solution:

It is given that

\begin{bmatrix} 2 & 2 & 3 \\ 7 & 1 & 1 \\ 0 & 6 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 3y+11 \\ 6z-1 \\ 5y+11 \end{bmatrix} + \begin{bmatrix} x \\ x \\ 4z \end{bmatrix} + \begin{bmatrix} z \\ 3x \\ 4y \end{bmatrix}

Solve the above matrix.

\begin{bmatrix} 2x+2y+3z \\ 7x+y+z \\ 6y+5z \end{bmatrix} = \begin{bmatrix} 3y+x+z+11 \\ 3x+x+6z-1 \\ 5y+4y+4z+11 \end{bmatrix}

\begin{bmatrix} 2x+2y+3z \\ 7x+y+z \\ 6y+5z \end{bmatrix} = \begin{bmatrix} x+3y+z+11 \\ 4x+6z-1 \\ 9y+4z+11 \end{bmatrix}

On comparing

x - y + 2z = 11

3x + y - 5z = -1

-3y + z = 11

From above three equations,

x = 4, y = -3, z = 2

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