Question

Write matrix to represent system 2a-3b=6,a=b=2

Answer 1

The matrix that represent the system 2a-3b=6,a=b=2. The given system of equation is a bit vague due to a=b=2. So the matrix that will represent is:

|2  -3  6|

|     1   2|

But if the equal sign is either a plus or a minus, the matrix will change to:

|2    -3      6|

|1  +/- 1   2|

Answer 2

A matrix is an array of numbers. So, we can talk about one matrix or several matrices. So, we have the following system of equations (I have corrected the second equation):

$\left \{ {{2a-3b=6} \atop {a+b=2}} \right.$

This system can be written using matrices as follows:

$\mathbf{Ax}=\mathbf{B}$

Where:

$\mathbf{A}=\left[\begin{array}{cc}2&-3\\1&1\end{array}\right]$

This one has 2 Rows and 2 Columns (that is, a 2 x 2 matrix). On the other hand, $\mathbf{x}$ is a column vector (that is, a 2 x 1 matrix):

$\mathbf{x}=\left[\begin{array}{c}a\\b\end{array}\right]$

Finally, $\mathbf{B}$ is a column vector (that is, a 2 x 1 matris)

$\mathbf{B}=\left[\begin{array}{c}6\\2\end{array}\right]$

So the system is written using matrices as follows:

$\mathbf{A}\mathbf{x}=\mathbf{B} \\ \\ \left[\begin{array}{cc}2&-3\\1&1\end{array}\right]\left[\begin{array}{c}a\\b\end{array}\right]=\left[\begin{array}{c}6\\2\end{array}\right]$