a Use the Matlab invn function to find the inverse of the fo

(a) Use the Matlab inv(n) function to find the inverse of the four matrices above.

(b) What special form, if any, do the inverses have? Be specific.

Your answer here should be a Matlab diary or script for part (a) showing how you entered or constructed the matrices, the statement finding the inverse, and then the Matlab output for each. You answer for part (b) should be a typed description of inverses’ form. Make sure to include all this in your Matlab submission file.

1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 (1 1). 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0

Solution

a)

>> n=[1 1;0 1]

n =

1 1
0 1

>> inv(n)

ans =

1 -1
0 1

>> n=[1 1 0;0 1 1;0 0 1]

n =

1 1 0
0 1 1
0 0 1

>> inv(n)

ans =

1 -1 1
0 1 -1
0 0 1

>> n=[1 1 0 0;0 1 1 0;0 0 1 1;0 0 0 1]

n =

1 1 0 0
0 1 1 0
0 0 1 1
0 0 0 1

>> inv(n)

ans =

1 -1 1 -1
0 1 -1 1
0 0 1 -1
0 0 0 1

>> n=[1 1 0 0 0;0 1 1 0 0;0 0 1 1 0;0 0 0 1 1;0 0 0 0 1]

n =

1 1 0 0 0
0 1 1 0 0
0 0 1 1 0
0 0 0 1 1
0 0 0 0 1

>> inv(n)

ans =

1 -1 1 -1 1
0 1 -1 1 -1
0 0 1 -1 1
0 0 0 1 -1
0 0 0 0 1

b)the inverse of matrix is follow one form

that is the diagonal of the matrix always 1\'s. from the diagonal to upper side of the matrix follow +1 diagonal next -1 diagonal alternatively.

1 -1
0 1

1 -1 1
0 1 -1
0 0 1

1 -1 1 -1
0 1 -1 1
0 0 1 -1
0 0 0 1

1 -1 1 -1 1
0 1 -1 1 -1
0 0 1 -1 1
0 0 0 1 -1
0 0 0 0 1