How do you solve a 4x4 Matrix?

You can in many ways

what is one way?

Inverse solving

could you explain?

Gaussian Elimination

4 x 4 ? a b c d e f g h i j k l m n o p it it (afkp) + (bglm) + (chin) + (ejod) - (dgjm) - (hkna) - (cfip) - (belo) ???? I hope I made the question clear enough to not take up too much of your time. http://www.math.ubc.ca/~israel/applet/mcalc/matcalc.html (matrices calculator.)

thanx beehive

imranmeah91 could you explain the Gaussian Elimination

Hold on

k thanx

\[\begin{array}c a&b&c&d\\ e&f&g&h\\ i&j&k&l\\ m&n&o&p\\ \end{array}\] \[\begin{array}c a&b&c&d\\ e&f&g&h\\ i&j&k&l\\ m&n&o&p\\ \end{array}\*] <- remove the * to format

amistre64: i didnt understand that

Hold on, I am trying to format

that is the code you type in to format a matrix so its readable

copy it into where?

we will just try to solve 2 by 2 matrix 2x+3y=2 -2x+x=6

but i want to know how to solve it by hand

i understand a 2x2 matrix imranmeah91 but i need a 4x4

\[\left( \begin{array}{cc} 2 & 3 \\ -2 & 1 \end{array} \right)|\left( \begin{array}{c} 2 \\ 6 \end{array} \right)\]

wait...not a system of equations by matrices... just a 4x4

Just 4 x 4 ? then what would you be finding?

the determinant

sry i should have said that earlier

no problem

got any input values in specific?

amistre64: not rele

\[\left( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 12 & 11 & 10 & 9 \\ 1 & 3 & 2 & 7 \end{array} \right)\]

that det() = 0 on my ti83

so how do you solve it?

Use coefficient rule \[\left( \begin{array}{ccc} 6 & 7 & 8 \\ 11 & 10 & 9 \\ 3 & 2 & 7 \end{array} \right)-2\left( \begin{array}{ccc} 5 & 7 & 8 \\ 12 & 10 & 9 \\ 1 & 2 & 7 \end{array} \right)+3\left( \begin{array}{ccc} 5 & 6 & 8 \\ 12 & 11 & 9 \\ 1 & 3 & 7 \end{array} \right)-4\left( \begin{array}{ccc} 5 & 6 & 7 \\ 12 & 11 & 10 \\ 1 & 3 & 2 \end{array} \right)\]

Now break it apart once more

?

\[1\left(6\left( \begin{array}{cc} 10 & 9 \\ 2 & 7 \end{array} \right)-7\left( \begin{array}{cc} 11 & 9 \\ 3 & 7 \end{array} \right)+8\left( \begin{array}{cc} 11 & 10 \\ 3 & 2 \end{array} \right)\right)-2\left(5\left( \begin{array}{cc} 10 & 9 \\ 2 & 7 \end{array} \right)-7\left( \begin{array}{cc} 12 & 9 \\ 1 & 7 \end{array} \right)+8\left( \begin{array}{cc} 12 & 10 \\ 1 & 2 \end{array} \right)\right)+3\left(5\left( \begin{array}{cc} 11 & 9 \\ 3 & 7 \end{array} \right)-6\left( \begin{array}{cc} 12 & 9 \\ 1 & 7 \end{array} \right)+8\left( \begin{array}{cc} 12 & 11 \\ 1 & 3 \end{array} \right)\right)-4\left(5\left( \begin{array}{cc} 11 & 10 \\ 3 & 2 \end{array} \right)-6\left( \begin{array}{cc} 12 & 10 \\ 1 & 2 \end{array} \right)+7\left( \begin{array}{cc} 12 & 11 \\ 1 & 3 \end{array} \right)\right)\]

kk i get it thanx a lot imranmeah91

hey btw how do i give a medal?

click the good answer next to my name

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