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Ex5. Simple linear algebra (15 marks)

(* Update: For this problem, the submitted file should be named ex5.m.*)

Get two square matrices \(A\) and \(B\) of the same size from user input. Output the following in the given order:

1. Their element-wise sum \(A+B\).

2. Their element-wise product of \(A\) and \(B\), i.e. \(C\) where \(c_{ij}=a_{ij}\cdot b_{ij}\).

3. Their matrix product \(AB\).

4. \(C\) where \(c_{ij} = 2 a_{ij}\).

5. The element-wise square of \(A\), i.e. \(C\) where \(c_{ij} = a_{ij}^2\).

6. The (matrix) product of \(B\) with itself, i.e. \(B^2\).

7. Their horizontal concatenation, i.e., put \(A\) on the left and \(B\) on the right, side by side, to form a new matrix.

8. Their vertical concatenation, i.e., put \(A\) on top of \(B\), side by side, to form a new matrix.

Sample Test Case

Input:

[3,6,2.2;1,4.5,10;7,7.1,0]
[5,1.3,2.9;1,4,-6;-2.9,8,4]

Output:

    8.0000    7.3000    5.1000
    2.0000    8.5000    4.0000
    4.1000   15.1000    4.0000

   15.0000    7.8000    6.3800
    1.0000   18.0000  -60.0000
  -20.3000   56.8000         0

   14.6200   45.5000  -18.5000
  -19.5000   99.3000   15.9000
   42.1000   37.5000  -22.3000

    6.0000   12.0000    4.4000
    2.0000    9.0000   20.0000
   14.0000   14.2000         0

    9.0000   36.0000    4.8400
    1.0000   20.2500  100.0000
   49.0000   50.4100         0

   17.8900   34.9000   18.3000
   26.4000  -30.7000  -45.1000
  -18.1000   60.2300  -40.4100

    3.0000    6.0000    2.2000    5.0000    1.3000    2.9000
    1.0000    4.5000   10.0000    1.0000    4.0000   -6.0000
    7.0000    7.1000         0   -2.9000    8.0000    4.0000

    3.0000    6.0000    2.2000
    1.0000    4.5000   10.0000
    7.0000    7.1000         0
    5.0000    1.3000    2.9000
    1.0000    4.0000   -6.0000
   -2.9000    8.0000    4.0000