Question

Rewrite the system of linear equations as a matrix equation AX = B.

x1 + 2x2 + 5x3 = 5

x1 + x2 + x3 = 6

4x1 + 6x2 + 5x3 = 7

Answer 1

`\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]`

Explanation:

Let's find the answer.

Because we have 3 equations and 3 variables (x1, x2, x3) a 3x3 matrix (A) can be constructed by using their respectively coefficients.

Equations:

Eq. 1 : x1 + 2x2 + 5x3 = 5

Eq. 2 : x1 + x2 + x3 = 6

E1. 3 : 4x1 + 6x2 + 5x3 = 7

Coefficients for x1 ; x2 ; x3

From eq. 1 : 1 ; 2 ; 5

From eq. 2 : 1 ; 1 ; 1

From eq. 3 : 4 ; 6 ; 5

So matrix A is:

`\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]`

And the vector of vriables (X) is:

`\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]`

Now we can find the resulting vector (B) using the 'resulting values' from each equation:

`\left[\begin{array}{ccc}5\\6\\7\end{array}\right]`

In conclusion, AX=B is:

`\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]`