Answer to Question #298635 in Linear Algebra for shahana

Question

Solve the given linear system by any method. 3x1 + X2 + X3 + X4 = 0, 5x1 - X2 + X3 - X4 = 0

Answer 1

$\begin{bmatrix} 3& 1&1&1 \\ 5&-1&1&-1 \end{bmatrix}\begin{bmatrix} x_1 \\ x_2\\x_3\\x_4 \end{bmatrix}=0$

$\frac{1}5R_2,\frac{1}3R_1$

$\begin{bmatrix} 1& ⅓&⅓&⅓ \\ 1 & -\frac{1}5&\frac{1}5&-\frac{1}5 \end{bmatrix}$

$\frac{-15}8(R_2-R_1)$

$\begin{bmatrix} 1& ⅓&⅓&⅓\\ 0&1 & ¼&1 \end{bmatrix}$

$R_1-⅓R_2$

$\begin{bmatrix} 1& 0&¼&0 \\ 0 & 1&¼&1 \end{bmatrix}$

$x_1+¼x_3=0$

$x_2+¼x_3+x_4=0$

$x_1=-¼x_3$

$x_2=-¼x_3-x_4$