For each of the questions, you will need to start with the original copy of 'a'
or 'M'

Manipulating Vectors

1. a([3 6 9]) = [];

or a(3:3:length(a)) = [];

2. a(3:3:length(a)) = 3:3:length(a);

3. a(a<0) = 0;

4. a(a<0) = a(a<0) * -2;

5. sum(a>0);

6. a' * a;

Manipulating Matrices

1. M(2:2:length(M), : ) = [];

2. M(:, [5 10]) = 0;

3. M - diag(diag(M));

4. M - diag(diag(M)) + 5 * eye(length(M));

5. M + diag(diag(M));

6. tril(M);

7. tril(M) + tril(M)' - diag(diag(M));

8. max(M, [], 2)  or  max(M')'

(max normally operates over columns, rather than rows)

9. sum( M(diag(M)>0, : ) );

Matrix Operations

1. M1 - rotation 90 degrees anticlockwise
   M2 - reflection in the line y=x
   M3 - stretch x-axis by 3
   M4 - project onto the y-axis

2. It's a rotation of 90 degrees clockwise.  If you reflect in the line y=x, then
rotate 90 degrees anticlockwise, then reflect agin in y=x, this is the result.

3. [ 1 0 0 0
     0 0 0 0
     0 0 1 0
     0 0 0 0 ]

4. A 2x2 matrix with every element 1/sqrt(2)