Graphical Construction of a 2x2 Matrix and Its Inverse

​
original matrix
A =
1
3
10
3
10
1
inverse matrix
-1
A
=
100
91
-
30
91
-
30
91
100
91
This Demonstration shows a pictorial representation of the relationship between a 2×2 matrix and its inverse. Drag the locators to determine two points; these define two vectors from the origin. The matrix
A
has those vectors as its rows; it is shown on the lower left.
The inverse matrix
-1
A
is then shown on the lower right. The columns of the inverse matrix can be constructed from the two dashed vectors. The blue row of
A
is orthogonal to the blue column of
-1
A
and the red row of
A
is orthogonal to the red column of
-1
A
.
If no inverse to
A
exists, this is indicated by "matrix is singular".

Details

This was a project for Advanced Topics in Mathematics II, 2017–2018, Torrey Pines High School, San Diego, CA.

External Links

Matrix (Wolfram MathWorld)
Matrix Inverse (Wolfram MathWorld)

Permanent Citation

Jodie Hoh
​
​"Graphical Construction of a 2x2 Matrix and Its Inverse"​
​http://demonstrations.wolfram.com/GraphicalConstructionOfA2x2MatrixAndItsInverse/​
​Wolfram Demonstrations Project​
​Published: April 6, 2018