Question

Which matrix represents the system of equations below? { -2x-7y=3 7x-6y=12

Answer 1

[-12x-13y+13z=15 
[7x-10y-3x=11 
[7x+14y+5z=-5 

Answer 2

A system of linear equations can be represented in matrix form using a coefficient matrix, a variable matrix, and a constant matrix.

Consider the given system of equations,

$-2x-7y=3$

$7x-6y=12$

The coefficient matrix can be formed by aligning the coefficients of the variables of each equation in a row. Each of the equation is written in standard form with the constant term on right side.

Therefore, the coefficient matrix for the above system is:

$\left[\begin{array}{ccc}-2&-7\\7&-6\\\end{array}\right]$

We have variables as x and y . So the variable matrix is $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$.

The constant terms of the equations, on the right side of the equality are 3 and 12 . The two numbers in that order correspond to the first and second equations, and therefore it take the places at the first and the second rows in the constant matrix. So, the matrix becomes $\left[\begin{array}{ccc}3\\12\\\end{array}\right]$ .

So, the system can be represented as:

$\left[\begin{array}{ccc}-2&-7\\7&-6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}3\\12\\\end{array}\right]$.