I'M CODING IN UNIX TERMINAL ON MAC. USING TEXTMATLAB. Thanks!!

10 How to Find Basis for ROW SPACE of AB Using Column Space of (AB)t = (AB)

3 9 7 2 6 3 1 LetABbedefinedasbefore. AB= 2 6 0 8 4 12 4

Type :

ABR = rref(AB)

To see the Reduced Row-Echelon Form of AB. Use ABR to find a basis for Column space of AB

Then enter your basis vectors as:

26 518433113 9 2 8 6 18 6

Note that row space of AB = column space of (AB).

Use MATLAB to find a basis for the row space of AB consist of row vectors of AB. Then enter your basis vectors as:

% ABV1 = Type your first row vector of basis of AB % ABV2 = Type your second row vector of basis of AB % ABV3 = Type your third row vector of basis of AB

11 How to Find independent Columns of Matrix AB 3 9 7 2 6 3 1

LetABbedefinedasbefore. AB= 2 6 0 8 4 12 4 26 51843311

3 9 2

8 6 18 6

% ABW1 = Type your first column vector of basis of AB % ABW2 = Type your second column vector of basis of AB % ABW3 = Type your third column vector of basis of AB

Now type

[R1, pivcol ] = rref(AB)

This command will provide you rref(AB) and pivot columns of AB. The columns of ABthat are independent and form a basis for the column space. You can use MATLAB to give you a matrix composed of the independent columns ofAB

Type:

UAB = AB(:,pivcol)

20

12 How to Find independent Columns of Matrix AB

You may use this to find a basis for the row space: Type:

[R2, pivcol ] = rref(AB)

This command will provide you rref(AB) and pivot columns of AB which are row vec- tors of AB. The columns of AB that are independent and form a basis for the column space.

Then enter your basis vectors as:

% ABU1 = Type your first Row vector of basis of AB % ABU2 = Type your second Row vector of basis of AB % ABU3 = Type your third Row vector of basis of AB

Note that these are Rows of AB that form a basis for row space of AB.

You Can use MATLAB to give you a matrix composed of the independent rows of ABType:

C = AB UAB1 = C(:,pivcol)