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  • Examine the consistency of the system of equations x + 2y = 2, 2x + 3y 3=3.

Q : 1        Examine the consistency of the system of equations.

                    \small x+2y=2

                    \small 2x+3y=3

Answers (1)

best_answer

We have given the system of equations:18967

                                         \small x+2y=2

                                       \small 2x+3y=3

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

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

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

|A| = 1(3) -2(2) = -1 \neq 0

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

Hence, the given system of equations is consistent.

 

 

Posted by

Divya Prakash Singh

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