Cramers Rule Problem

[Jason76]

First of all I need to be able to write a matrix.

Here I will try without Latex

-x + 2y - 3z = 1

2x + 0 + z = 0

3x = 4y + 4z = 2


|A| =

-1 2 -3

2 0 1

3 -4 4

= 10

Because (using cofactor method for top row)

Det 1 =

0 1

-4 4 = 4

Det 2

2 1

3 4

= 5

Det 3

2 0

3 -4

= -8

Row = 4 5 -8 After Co-factor pattern (+ - +) you have 4 -5 -8

Finding Det A = [(-1)4] + [2 (-5)] + [-3 (-8)] = 10 (This is correct in the book)

First need to know how to proceed in Latex to continue with the next steps.

Find x_{1}

Det |x_1 stuff|

1 2 -3

0 0 1

2 -4 -4

Det 1

0 1

-4 -4 = 4


Det 2

0 1

2 -4 = -2

Det 3

0 0

2 -4 = 0

Pattern

4 -2 0

After applying cofactor pattern:

-4 2 0

Det x_1 stuff = [-4(-1)] + [2(2)] + [0(-3)] = 8

x_{1} = et of x_{1} stuff / det |A| = 8/10 = 4/5 - answer correct on homework.

 

[stapel]

Are you saying that you have no problems with the exercise, that you're only needing help in formatting?

Thank you!

 

[Jason76]

Are you saying that you have no problems with the exercise, that you're only needing help in formatting?

Thank you!

I originally, thought I might have a problem, but I seem to be getting it OK now. However, I would like to know how to display matrices on this forum, using Latex.

 

[Deleted member 4993]

I originally, thought I might have a problem, but I seem to be getting it OK now. However, I would like to know how to display matrices on this forum, using Latex.

Do a google search - you'll find it!!!

 

[Jason76]

\(\displaystyle \left| \begin{array}{cc} -x & + & 2y & - & 3z & = & 1 \\ 2x & + & 0 & + & z & = & 0 \\ 3x & + & 4y & + & 4z & = & 2 \end{array} \right|\)


\(\displaystyle |A| =\)

\(\displaystyle \left| \begin{array}{cc}- 1 & 2 & - 3 \\ 2 & 0 & 1\\ 3 & - 4 & 4 \end{array} \right|\)

\(\displaystyle = 10\)

Because (using cofactor method for top row)

Det 1 =

\(\displaystyle \left| \begin{array}{cc} 0 & 1 \\-4 & 4 \end{array} \right|\)

\(\displaystyle = 4\)

Det 2

\(\displaystyle \left| \begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array} \right|\)

\(\displaystyle = 5\)

Det 3

\(\displaystyle \left| \begin{array}{cc} 2 & 0 \\ 3 & -4 \end{array} \right|\)

\(\displaystyle = -8\)

Row = \(\displaystyle \left| \begin{array}{cc} 4 & 5 & -8 \end{array} \right|\) After Co-factor pattern (+ - +) you have \(\displaystyle \left| \begin{array}{cc} 4 & -5 & 8 \end{array} \right|\)

Finding Det A \(\displaystyle = [(-1)4] + [2 (-5)] + [-3 (-8)] = 10 \)(This is correct in the book)

First need to know how to proceed in Latex to continue with the next steps.

Find \(\displaystyle x_{1}\)

Det |x_1 stuff|

\(\displaystyle \left| \begin{array}{cc} 1 & 2 & -3 \\0 & 0 & 1\\ 2 & -4 & -4\end{array} \right|\)

\(\displaystyle Det 1\)

\(\displaystyle \left| \begin{array}{cc} 0 & 1 \\-4 & 4 \end{array} \right|\)

\(\displaystyle = 4\)


Det 2

\(\displaystyle \left| \begin{array}{cc} 0 & 1 \\2 & - 4 \end{array} \right|\)

\(\displaystyle = -2\)

Det 3

\(\displaystyle \left| \begin{array}{cc} 0 & 0 \\2 & -4 \end{array} \right|\)

\(\displaystyle = 0\)

Pattern

\(\displaystyle \left| \begin{array}{cc} -4 & -2 & 0 \end{array} \right|\)

After applying cofactor pattern:

\(\displaystyle \left| \begin{array}{cc} -4 & 2 & 0 \end{array} \right|\)

Det x_1 stuff \(\displaystyle = [-4(-1)] + [2(2)] + [0(-3)] = 8\)

\(\displaystyle x_{1}\) = Det of \(\displaystyle x_{1}\) stuff \(\displaystyle / det |A| = 8/10 = 4/5 \)- answer correct on homework.

 

[HallsofIvy]

There is a Latex tutorial at
http://www.cs.cornell.edu/info/misc/latex-tutorial/latex-home.html