Question

Consider the system of equations given. 3x + 3y + z = −1 2x + 3y + z = −3 2x − 2y + z = −3 (a) Write a matrix equation (in the form AX = B) that is equivalent to the system of linear equations. (Use the order of the equations to write the matrix.)

Answer 1

`\begin{bmatrix}3 &3& 3\\ 2 & 3& 1\\ 2 & -2& 1\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}-1\\ -3\\ -3\end{bmatrix}`

Explanation:

We have given system of equation

3x+3y+z= -1

2x+3y+z= -3

2x-2y+z= -3

We have to write matrix equation in form of AX=B

The matrix equation will be

`\begin{bmatrix}3 &3& 3\\ 2 & 3& 1\\ 2 & -2& 1\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}-1\\ -3\\ -3\end{bmatrix}`

Here in A matrix first row is coefficient of x second row is coefficient of y and third row is coefficient of z

Matrix B is a constant matrix and matrix X is variable matrix