213 - A4.7 - Variable in Matrix -- Sage

var('b') A = matrix([[-3,-2,-2],[-7,-2,-4],[-1,5+b,0]]) show(A) show(A.echelon_form())

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} -3 & -2 & -2 \\ -7 & -2 & -4 \\ -1 & b + 5 & 0 \end{array}\right)$

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right)$

var('b,c') A = matrix([[-3,-2,-2,1],[-7,-2,-4,1],[-1,5+b,0,1]]) show(A) show(A.echelon_form())

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} -3 & -2 & -2 & 1 \\ -7 & -2 & -4 & 1 \\ -1 & b + 5 & 0 & 1 \end{array}\right)$

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 1 & 0 & 0 & \frac{b + 7}{b + 3} \\ 0 & 1 & 0 & \frac{b + 7}{2 \, {\left(b + 3\right)}} - \frac{1}{2} \\ 0 & 0 & 1 & -\frac{2 \, {\left(b + 7\right)}}{b + 3} \end{array}\right)$

var('a,b,c,h') A = matrix([[1,-5,1],[-1,7,1],[3,8,h]]) show(A) show(A.echelon_form())

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 1 & -5 & 1 \\ -1 & 7 & 1 \\ 3 & 8 & h \end{array}\right)$

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right)$

var('a,b,c,h') A = matrix([[1,-5,1,a],[-1,7,1,b],[3,8,h,c]]) show(A) show(A.echelon_form())

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 1 & -5 & 1 & a \\ -1 & 7 & 1 & b \\ 3 & 8 & h & c \end{array}\right)$

$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 1 & 0 & 0 & \frac{7}{2} \, a + \frac{5}{2} \, b + \frac{3 \, {\left(29 \, a + 23 \, b - 2 \, c\right)}}{h - 26} \\ 0 & 1 & 0 & \frac{1}{2} \, a + \frac{1}{2} \, b + \frac{29 \, a + 23 \, b - 2 \, c}{2 \, {\left(h - 26\right)}} \\ 0 & 0 & 1 & -\frac{29 \, a + 23 \, b - 2 \, c}{2 \, {\left(h - 26\right)}} \end{array}\right)$

# change to octave mode before evaluating this cell A = [1 -5 1; -1 7 8; 3 8 6] rref(A)

213 - A4.7 - Variable in Matrix

1923 days ago by Professor213