2-8-19

 

 

 

 

Matrix Calculations

 

 

 

 

 

 

uMatrix Inversion

 

 

[OPTN]-[MAT]-[x–1]

Example

To invert the following matrix :

 

Matrix A =

 

1

2

 

 

 

 

 

 

 

 

3

4

 

 

 

 

 

 

 

K2(MAT)1(Mat) av(A)!)(x–1) w

uSquaring a Matrix

 

 

[OPTN]-[MAT]-[x2]

Example To square the following matrix :

Matrix A =

 

1

2

 

 

 

 

 

 

3

4

 

 

 

 

 

 

 

 

 

 

K2(MAT)1(Mat)av(A)xw

#Only square matrices (same number of rows and columns) can be inverted. Trying to invert a matrix that is not square produces an error.

#A matrix with a determinant of zero cannot be inverted. Trying to invert a matrix with determinant of zero produces an error.

#Calculation precision is affected for matrices whose determinant is near zero.

#A matrix being inverted must satisfy the conditions shown below.

A A–1= A–1A = E =

 

1

0

 

 

0

1

The following shows the formula used to invert Matrix A into inverse matrix A–1.

A =

 

a

b

 

 

 

 

 

 

c

d

 

 

 

 

 

 

 

 

 

 

A–1=

 

 

1

 

 

 

 

d –b

 

 

 

 

 

 

 

ad – bc

 

 

 

–c a

 

 

 

 

 

Note that ad – bc G0.

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