3x3 Matrix Explorer

(1,1)

(1,2)

(1,3)

(2,1)

(2,2)

(2,3)

(3,1)

(3,2)

(3,3)

integer entriesin matrix

Matrix

Transpose

Inverse

0	3	2
2	1	3
3	2	1

0	2	3
3	1	2
2	3	1

-0.22	0.04	0.30
0.30	-0.26	0.17
0.04	0.39	-0.26

Trace	Determinant	Rank
2	23	3

Eigenvalues

Eigenvectors

5.69

-1.85+0.79

-1.85-0.79

-0.43-0.42	-0.28+0.37	0.65
-0.43+0.42	-0.28-0.37	0.65
0.53	0.61	0.60

The transpose of a matrix

A

is a matrix

T

A

whose

th

i

column is equal to the

th

i

row of

A

.

The inverse of a

3×3

matrix

A

is a matrix

-1

A

such that

A

-1

A

is the identity matrix.

The trace of a matrix is the sum of the entries on the main diagonal (upper-left to lower-right).

The determinant is computed from all the entries of the matrix and is nonzero precisely when the matrix is nonsingular, that is, when the equation

Ax=b

always has a unique solution.

The matrix rank is the number of linearly independent columns and is equal to three precisely when the matrix is nonsingular.

A number

λ

is an eigenvalue of

A

if there is some nonzero vector

x

such that

Ax=λx

; the vector

x

is called an eigenvector. In the result, the

th

i

row of the eigenvector array is an eigenvector of unit length associated with the

th

i

eigenvalue in the eigenvalue array.