Inverse Matrices

What is the determinant of a matrix

ad - bc

Singular matrix

The determinant is 0

Non-singular matrix

The determinant is not 0

Explain why certain matrices don’t have inverses

They are singular, so they have a determinant of 0. 1/determinant is used to find the inverse and 1/0 is not conformable

A^-1A

I

A^-1BA

Not B as matrix multiplication is not commutative

A^-1AB

B

Which type of matrices have a determinant

Square matrices

How to find the inverse of a 2×2 matrix

1/determinant x (d -b )

. (-c a )

Acronym for finding the inverse of a 3×3 matrix

DMCAR

What does the inverse of a 3×3 matrix acronym stand for

D- Determinant

M- Matrix of Minors

C- Matrix of Cofactors

A- Adjugate

R- Reciprocal

How to find the determinant of a 3×3 matrix

a|minor| -b|minor| +c|minor|

What does |M| mean in matrices

The determinant of M

Minor matrix

The determinant of the 2×2 matrix created by crossing out the row and column the element is in

How to find the inverse of a 3×3 matrix

1- Find the determinant

2- Find the determinant of the minor matrix for each element to form a matrix made up of these determinants

3- Multiply by the matrix: (+ - + )

. (- + - )

. (+ - + )

4- Reflect each element in the identity line (elements in the identity line don’t move)

5- Multiply by the reciprocal of the determinant