2-Matrix Operation

Matrix Mutiplication¶

• 

Interpret by column¶

• We could consider it as A * a set of column vectors, since each column of C only depends on A * each column of B

• For example

Interpret by row¶

• Rows of C are combination of rows of B

• For example

Another mutiplication rule¶

• $Z$ = Column of $A$ * Row of $B$

• Example

• 

The Laws for Matrix Operations¶

About addition¶

About multiplication¶

About Powers¶

Block multiplication¶

Inverse¶

Example¶

property¶

Two ways to solve the inverse¶

Solve them by the meaning¶

Gauss -Jordan (Augmented matrix)¶

Singular matrix (do not have inverse)¶

Gauss-Jordan function to get inverse (solve two eqs at once)¶

Important Example¶