Hey everyone I'm practicing some linear equation matrix questions, so far they're easy to construct, but I am completely lost on this one since I cannot use the method of putting them in separate columns like the normal technique used. Where do I start with this question, please anyone give me guidance?
(a) Consider the system of linear equations given by
$_1 = −x_2$
$200 x_3 = 200$
$x_3 = 4 − 3 x_4$
$100 x_2 + 100 x_3 = 100$
(i) Write the above system of equations in matrix form.
On
Welcome to Math.SE. I hope you are not asking your HW question.
You can collate all the variables to one-side and constants to the other as
$\begin{bmatrix} 1&1&0&0\\0&0&200&0\\0&0&1&3\\0&100&100&0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\\x_4\end{bmatrix}=\begin{bmatrix}0\\200\\4\\100\end{bmatrix},$
thereby, forming a set of linear equation in a matrix form $Ax=b.$
Use $1x_1 +(-1)x_2 + 0x_3 + 0x_4 = 0$ for the first row (that is $(1, -1, 0, 0)$), $0x_1 +0x_2 + 200x_3 + 0x_4 = 200$ for the second, $0x_1 +0x_2 + 1x_3 + 3x_4 = 4$ for the third, and $0x_1 +100x_2 + 100x_3 + 0x_4 = 100$ for the last.