We have seen how one can access a subset of a list by providing a list of desired positions:

```
>> A=rand(1,5)
A =
0.6430 0.5461 0.5027 0.0478 0.2289
>> A([2 3 1 1])
ans =
0.5461 0.5027 0.6430 0.6430
```

There are a few more extensions of this:

It can be used to modify part of a matrix:

`%with A as before: `

>> A([1 2])=3+A([3 4])
A =
3.5027 3.0478 0.5027 0.0478 0.2289
%or even:
>> A([3 4])=1
A =
3.5027 3.0478 1.0000 1.0000 0.2289

Additionally, this works for matrices and submatrices as well:

```
>> A=magic(4)
A =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
>> A([2 3], [1 4])
ans =
5 8
9 12
>> A(1:2,3:4)=1
A =
16 2 1 1
5 11 1 1
9 7 6 12
4 14 15 1
```

The keyword `end`

will evaluate to the size of the dimension of the matrix in which it is located:

```
>> A=magic(4);
>> A(end,end)
ans =
1
>> A([1 end],[1 end])
ans =
16 13
4 1
>> A([1 end/2], [2, end-1])
ans =
2 3
11 10
>> A(2,1:end)
ans =
5 11 10 8
>> A(1:end,3)
ans =
3
10
6
15
% 1:end is so useful that it has an even shorter notation, :
>> A(:,1)
ans =
16
5
9
4
>> A(4,:)
ans =
4 14 15 1
```

Finally, a matrix can be accessed with a single index (as opposed to with two) and this implies a specific ordering of the elements (rows first, then columns):

```
>> A(5)
ans =
2
>> A(4:10)
ans =
4 2 11 7 14 3 10
>> A(:)
ans =
16
5
4
2
11
7
14
3
10
6
15
13
8
12
1
```

**Exercise 9:** *Practice some of these methods for accessing matrix elements with the following exercises:*

*Create a matrix of size*\(N\times N\)*that has ones in the border and zeros inside. For example if*\(N=3\)*the matrix can be created with*

```
>> A=ones(3,3); A(2,2)=0
A =
1 1 1
1 0 1
1 1 1
```

*Make this construction depend on* \(N\) *and work for any positive integer* \(N\ge2\)

*Create a 5x5 matrix whose rows are (1:5)*

*Extract the diagonal of a given matrix without using*

`diag`

*(you may use*

`size`

*)*

*Flip a given matrix horiztonally. Vertically? Do not use*

`fliplr`

*or*

`flipud`

*Extract the anti-diagonal of a given matrix*

*Extract the anti-diagonal, without first flipping it (Hint: use single index access)*