3x3 Matrix Transpose, Inverse, Trace, Determinant and Rank

​
(1,1)
1
(1,2)
2
(1,3)
3
(2,1)
2
(2,2)
1
(2,3)
3
(3,1)
3
(3,2)
2
(3,3)
1
integer entries in matrix
matrix
transpose
inverse
​
​
​
​
​
1
2
3
2
1
3
3
2
1
1
2
3
2
1
2
3
3
1
-0.42
0.33
0.25
0.58
-0.67
0.25
0.08
0.33
-0.25
trace
determinant
rank
​
​
​
3
12
3
The transpose of a matrix
A
is a matrix
A
whose rows and columns are reversed.
The inverse of a
3×3
matrix
A
is a matrix
-1
A
such that
A
-1
A
and
-1
A
A
equal the identity matrix. If the inverse exists, the matrix is said to be nonsingular.
The trace of a matrix is the sum of the entries on the main diagonal (upper left to lower right).
The determinant
Δ
is computed from all the entries of the matrix. The matrix
A
is nonsingular if and only if
Δ≠0
. In that case, the equation
Ax=b
has a unique solution.
The matrix rank is the number of linearly independent columns and is equal to three when the matrix is nonsingular.

External Links

Square Matrix (Wolfram MathWorld)
Matrix Inverse (Wolfram MathWorld)
Transpose (Wolfram MathWorld)
Matrix Trace (Wolfram MathWorld)
Determinant (Wolfram MathWorld)
Matrix Rank (Wolfram MathWorld)
3x3 Matrix Explorer

Permanent Citation

Chris Boucher
​
​"3x3 Matrix Transpose, Inverse, Trace, Determinant and Rank"​
​http://demonstrations.wolfram.com/3x3MatrixTransposeInverseTraceDeterminantAndRank/​
​Wolfram Demonstrations Project​
​Published: July 5, 2018