Solving Linear Systems with Matrix Inverses

$$\left[5\ \ 0\ \ -10\right]$$

$$\left[2\ \ 3\ \ -1\right]$$

$$\left[-6\ \ 1\ \ -4\right]$$

$$\left[5\ \ 0\ \ 0\right]$$

$$\left[2\ \ 3\ \ 0\right]$$

$$\left[2\ \ 3\ \ -1\right]$$

$$\left[-6\ \ 1\ \ -4\right]$$

$$\left[5\ \ 0\ \ 0\right]$$

$$\left[2\ \ 3\ \ 0\right]$$

$$\left[-6\ \ 1\ \ 4\right]$$

$$\left[-6\ \ 1\ \ -4\right]$$

$$\left[-6\ \ 0\ \ 4\right]$$

-10

-1

-11

-10 -1 -11

10

1

11

10 1 11

coefficient matrix is multiplied by the constant matrix

the inverse of the coefficient matrix is multiplied by the constant matrix

coefficient matrix is multiplied by the solution matrix

the inverse of the coefficient matrix is multiplied by the solution matrix

(3, 1, -5)

(-3, 1, -1)

not possible; the inverse does not exist

2nd

x^-1

alpha

zoom

$$\left[1\ \ 1\ \ 1\ \ -3\right]$$

$$\left[1\ \ -1\ \ 1\right]$$

$$\left[1\ \ -1\ \ 1\ \ -3\right]$$

$$\left[1\ \ 1\ \ 1\right]$$

$$\left[1\ \ -1\ \ -1\ \ 3\right]$$

$$\left[1\ \ -1\ \ -1\right]$$

$$\left[1\ \ 1\ \ 1\right]$$

$$\left[-3\ \ 1\ \ 1\right]$$

$$\left[5\ \ 5\ \ 1\right]$$

$$\left[5\ \ -5\ \ 1\right]$$

$$\left[5\ \ 5\ \ 0\ \ -15\right]$$

$$\left[5\ \ 5\ \ 1\ \ 15\right]$$

No Solution

(3,2,5)

Does not exist.

(5,-4,1)

(5,-7/3,0)

No Solution

Infinite Solution

(-5,7/3,0)