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  • Examine the consistency of the system of equations. 5x - y + 4z = 5, 2x + 3y + 5z = 2, 5x - 2y + 6z = -1

Q : 6       Examine the consistency of the system of equations.

               \small 5x-y+4z=5

               \small 2x+3y+5z=2

              \small 5x-2y+6z=-1

Answers (1)

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We have given the system of equations:

                                 \small 5x-y+4z=5

                               \small 2x+3y+5z=2

                              \small 5x-2y+6z=-1

The given system of equations can be written in the form of the matrix; AX =B

where A = \begin{bmatrix} 5& -1&4 \\ 2& 3& 5\\ 5& -2 &6 \end{bmatrix},  X = \begin{bmatrix} x\\y \\ z \end{bmatrix}  and B = \begin{bmatrix} 5\\2 \\ -1 \end{bmatrix}.

So, we want to check for the consistency of the equations;

|A| = 5(18+10) +1(12-25)+4(-4-15)

= 140-13-76 = 51 \neq 0 

Here A is non- singular matrix therefore there exist A^{-1}.

Hence, the given system of equations is consistent.

Posted by

Divya Prakash Singh

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