Question

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

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2x1 + 5x2 − 2x3 + x4 + 2x5 = 1
x1 + x2 − 2x3 + x4 + 4x5 = 5

Answer 1

Answer:

Given:  $\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}$

$2x_{1}+5 x_{2}  - 2_{3} + x_{4} + 2x_{5}\\[tex]

[tex]x_{1}+ x_{2}  - 2_{3} + x_{4} + 4x_{5}$

The system of linear equations in matrix form may be written as:

AX=B,

where,

A is coefficient matrix of order $2\times 4$ and is given by:

A = $\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}$

X is variable matrix of order  $5\times 1$ and is given by:

X=  $\begin{bmatrix}x_{_{1}}\\x_{_{2}}\\x_{3}\\x_{4}\\x_{5}\end{bmatrix}$

and B is the contant matrix of order $2\times 1$ and is given by:

B = $\begin{bmatrix}1\\5\end{bmatrix}$

Now, AX=B

$\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}$. $\begin{bmatrix}x_{_{1}}\\x_{_{2}}\\x_{3}\\x_{4}\\x_{5}\end{bmatrix}$ = $\begin{bmatrix}1\\5\end{bmatrix}$