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Linear Algebra

Inverse Is Undo

If A does not collapse area to zero, A⁻¹ can pull everything back.

What is inverse?

If A transforms the grid, can we undo it?

Before memorizing a formula, check whether the transform loses information.

Try different matrices

A

The left column is where i lands; the right column is where j lands.

det(A)1

Has an inverse because area remains

A⁻¹

1-1-12

det = 1, so no area is lost and undo is possible.

Before A

det = 1

A

After A

det = 1

A⁻¹

After undo

det = 1

A⁻¹A = I

Next, Ax=b:b is the destinationx is the point before AA⁻¹ undoes b to find x

Speed 1.0x

Credits & References