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# Exercise 1

Construct a 5 x 10 matrix A, for which every $$A_{ij} = i^j$$ Hint: remember that operations are cellwise in R.

# Exercise 2

Construct a 10 x 10 matrix A, for which $$A_{ij} = |i-j|$$. Then extract its diagonal Hint: remember that operations are cellwise in R.

# Exercise 3

Create a 10 x 10 matrix A, for which $$A_{ij} = (i-1)*10 + j$$ Hint: this is the easiest, you should just try to understand how this matrix should look like.

# Exercise 4

Consider the matrix of the previous exercise (3). Find a matrix B, for which $$B_{ij} = 2 \times A_{ij}$$. Find a matrix C, for which $$C_{ij} = i \times j \times A_{ij}$$

# Exercise 5

Create a list of 10 elements. Each element is a vector $$V_i = i, \quad i = 1 \ldots 10$$

# Exercise 6

Convert the previous list to a $$10 \times 10$$ matrix A, by row.

# Exercise 7

The same like exercise 6, by column.