Question

What is 5x+4y=-14, 3x+6y=6 in matrix

Answer 1

`\left[\begin{array}{ccc}5&4\\3&6\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}-14\\6\end{array}\right]` is the required matrix form.

Explanation:

Here, the given system of equation is:

5 x + 4 y = -14,

3 x + 6 y = 6

In a system of equation, the matrix for is given as

AX = b

Here, A = Co-efficient Matrix, X = Variable Matrix and B = Constant Matrix

Considering the given system:

Co-efficient Matrix(A) =
`\left[\begin{array}{ccc}5&4\\3&6\end{array}\right]`

Variable Matrix(X) =
`\left[\begin{array}{ccc}x\\y\end{array}\right]`

Constant Matrix(b) =
`\left[\begin{array}{ccc}-14\\6\end{array}\right]`

Hence, the combined matrix form of AX = b is

`\left[\begin{array}{ccc}5&4\\3&6\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}-14\\6\end{array}\right]`