Question

Use a matrix equation to solve the system of linear equations. left brace Start 2 By 1 Matrix 1st Row 1st Column 2nd Row 1st Column EndMatrix x plus 2 y equals 8 nbsp 2 x plus 6 y equals 9 What is the inverse​ matrix?

Answer 1

`\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]`

Explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

`\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]`

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

`A^(-1)` = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A =
`\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]`

`A^(-1)`=
`(1)/(2) \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]` =
`\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]`