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]`