1. ## find x

A = [4 3]
......[2 1]

If AX = [3 4]
..........[1 6]

Find X.

2. Originally Posted by DivideBy0
A = [4 3]
......[2 1]

If AX = [3 4]
..........[1 6]

Find X.
Use Gaussian ellimination on the augmented matrix:

Code:

[4 3 | 3 4]
[2 1 | 1 6]

[0 1 | 1 -8]
[2 1 | 1  6]

[0 1 | 1 -8]
[2 0 | 0 14]

[1 0 | 0  7]
[0 1 | 1 -8]

Now  check:

[4 3][0  7]  =  [3 4]
[2 1][1 -8]     [1 6]
RonL

3. Hello, DivideBy0!

Here's a primitive way to solve it . . .

A = [4 3]
. . . [2 1]

If AX = [3 4]
. . . . . .[1 6]

Find X.
Let X .= .| a b |
. . . - . . .| c d |

Then we have: . | 4 3 | . | a b | -= -| 3 4 |
. . . . . . . . . . . .| 2 1 | . | c d | . . . | 1 6 |

Hence: . | 4a + 3c . 4b + 3d | -= -| 3 4 |
. . - . - . | 2a + .c . .2b + -d | . . . | 1 6 |

And we have two system of equations:

. . 4a + 3c .= .3 . . . . 4b + 3d .= .4
. . 2a + .c -= -1 . . . . 2b + . d .= .6

Solve by your favorite method and get:

. . a = 0, .b = 7, .c = 1, .d = -8

4. A = [4 3]
. . . [2 1]

AX = [3 4]
. . . .[1 6]

A'AX = A' [3 4]
. . . . . . [1 6]
.....X.= [1 -3][3 4]
. . . . . [-2 4][1 6]

A'=A inverse

if A=[a b]
.....[c d]

A'=[d -b]
.....[-c a]

5. Hello, singular!

You left out the fraction . . .

. . . . . . | a b |
Given: . | . - .|
. . . . . . | c d |

. . . . - . . . . . . .| . . d . . . . .-b . - |
. . . . - . . . . . . .| -------- . --------- |
. . . . - . . . . . . .| ad - bc . ad - bc .|
The inverse is: . | . . . . . . . . . . . . |
. . . . - . . . . . . .|. . -c . . . . . a . . .|
. . . . - . . . . . . .| -------- . --------- |
. . . . - . . . . . . .| ad - bc . ad - bc .|

In baby-talk:
. . Switch the elements on the main (southeast) diagonal.
. . Change the signs of the elements on the other diagonal.
. . Divide all elements by the determinant of the matrix.

6. Originally Posted by Soroban
[size=3]Hello, singular!

You left out the fraction . . .
i'm so stupid......sorry...