Question

Find the matrix equation that represents the system:

Answer 1

Each of the given matrix equations does not represent this system of equations.

Explanation:

`\left\{\begin{array}{ccc}2x-3=2y\\y-5x=14\end{array}\right\\\\\text{Let's convert the system of equations to form}\\\\\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{array}\right\\\\\left\{\begin{array}{ccc}2x-3=2y&(1)\\y-5x=14&(2)\end{array}\right\\\\(1)\ 2x-3=2y\qquad\text{add 3 to both sides}\\2x=2y+3\qquad\text{subtract}\ 2y\ \text{From both sides}\\\boxed{2x-2y=3}\\(2)\ y-5x=14\\\boxed{-5x+y=14}\\\\\text{We get the system of equations in the form we need.}`

`\left\{\begin{array}{ccc}2x-2y=3\\-5x+y=14\end{array}\right\\\\\text{The first matrix is the matrix of coefficients at x and y.}\\\\\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\end{array}\right] \Rightarrow\left[\begin{array}{ccc}2&-2\\-5&1\end{array}\right]\\\\\text{The second matrix is the matrix:}\\\\\left[\begin{array}{ccc}x\\y\end{array}\right]\\\\\text{The third matrix is the matrix of numbers from the right side of the equation.}\\\\\left[\begin{array}{ccc}c_1\\c_2\end{array}\right]\Rightarrow\left[\begin{array}{ccc}3\\14\end{array}\right]`

`\text{Therefore we have:}\\\\\left[\begin{array}{ccc}2&-2\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}3\\14\end{array}\right]`