WOLFRAM|DEMONSTRATIONS PROJECT

3x3 Matrix Explorer

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(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.