- #1

TonyC

- 86

- 0

i.e. -10x - 6y = 6

7x + y = -7

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter TonyC
- Start date

- #1

TonyC

- 86

- 0

i.e. -10x - 6y = 6

7x + y = -7

- #2

Galileo

Science Advisor

Homework Helper

- 1,994

- 6

[tex]\left( \begin{array}{cc} -10 & -6 \\ 7 & 1\end{array}\right)\left( \begin{array}{c} x \\ y \end{array}\right)=\left( \begin{array}{c} 6 \\ -7 \end{array}\right)[/tex]

In general, you can write a linear system of n equations in n unknowns as a matrix equation Ax=b. If you can find the inverse of A (let's call it C, so that CA=AC=I) you have solved the problem, just put x=Cb, then A(Cb)=(AC)b=b.

- #3

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 970

- #4

TonyC

- 86

- 0

i.e. Cramer Method, Gaussian, elementary row operations. This one has me truly stumped. Maybe I'm too tied (or old) to grasp it today.

- #5

TonyC

- 86

- 0

Still trying to figure this out

- #6

VietDao29

Homework Helper

- 1,426

- 3

If:

[tex]A:= \left[ \begin{array}{cc} a & b \\ c & d \end{array} \right][/tex]

Then:

[tex]A ^ {-1}= \frac{1}{ad - bc} \left[ \begin{array}{cc} d & -b \\ -c & a \end{array} \right][/tex]

After finding the inverse of A, note that:

[tex]Ax = b \Leftrightarrow A ^ {-1}Ax = A ^ {-1}b \Leftrightarrow x = A ^ {-1}b[/tex]

Viet Dao,

- #7

amcavoy

- 665

- 0

[tex]\left[\begin{array}{cc|cc}a & b & 1 & 0 \\ c & d & 0 & 1\end{array}\right][/tex]

Use row operations to make the left side (your original matrix) the identity matrix, and what is left on the right will be the inverse. You are basically saying [itex]A\mathbf{x}=I\implies\mathbf{x}=A^{-1}[/itex].

- #8

neurocomp2003

- 1,366

- 3

SHOW YOUR WORK first.

- #9

TonyC

- 86

- 0

I posted the work I have been doing with Matrices previously, thanks for your concern

Share:

- Last Post

- Replies
- 16

- Views
- 447

- Last Post

- Replies
- 6

- Views
- 380

- Replies
- 2

- Views
- 251

- Last Post

- Replies
- 10

- Views
- 106

- Replies
- 14

- Views
- 514

- Replies
- 14

- Views
- 487

- Replies
- 13

- Views
- 506

- Replies
- 16

- Views
- 722

- Replies
- 1

- Views
- 564

- Replies
- 15

- Views
- 604