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

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]</p><p>[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* 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* 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* 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}`