Question

solve the equation by matrix method 2x+3y=9,-x+y=2​

Answer 1

Answer:

the answer is 567

Step-by-step explanation:

hope this was helpful

Answer 2

Answer:

     The value is $x=\frac{3}{5} , y=\frac{13}{5}$.

Step-by-step explanation:

        Write the equation in matrix form:

               $\left[\begin{array}{ccc}2&3\\-1&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}9\\2\\\end{array}\right]$

   Let multiply the equation by the inverse matrix of $\left[\begin{array}{ccc}2&3\\-1&1\\\end{array}\right]$.

          inverse$(\left[\begin{array}{ccc}2&3\\-1&1\\\end{array}\right])\left[\begin{array}{ccc}2&3\\-1&1\\\end{array}\right]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=$inverse$(\left[\begin{array}{ccc}2&3\\-1&1\\\end{array}\right])\left[\begin{array}{ccc}9\\2\\\end{array}\right]$

The product of a matrix and its inverse is the identity matrix.

          $\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=$inverse $(\left[\begin{array}{ccc}2&3\\-1&1\\\end{array}\right])\left[\begin{array}{ccc}9\\2\\\end{array}\right]$

For the 2×2 matrix $\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$, the inverse matrix is $\left[\begin{array}{ccc}\frac{d}{ad-bc} &\frac{-b}{ad-bc} \\\frac{-c}{ad-bc} &\frac{a}{ad-bc} \\\end{array}\right]$ so the matrix equation can be rewritten as a matrix multiplication problem.

                  $\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}\frac{1}{2-3(-1)} &-\frac{3}{2-3(-1)} \\\frac {1}{2-3(-1)} &\frac{2}{2-3(-1)} \\\end{array}\right]\left[\begin{array}{ccc}9\\2\\\end{array}\right]$

   Multiply the matrices

     $\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}\frac{1}{5} &-\frac{3}{5} \\\frac {1}{5} &\frac{2}{5} \\\end{array}\right]\left[\begin{array}{ccc}9\\2\\\end{array}\right]$

       $\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}\frac{3}{5} \\\frac {13}{5} \ \\\end{array}\right]$