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Loops
Use list comprehension to generate the list of all perfect numbers less than 10,000, \(\{P_1,P_2,\ldots,P_N\}\).
What is their sum \(\sum_i P_i\)?
Assumptions and Details
- A perfect number is any integer which is equal to the sum of its proper divisors (all its divisors except for itself).
Suppose you're working on code for a molecular dynamics visualization. You need to represent various matrices, like the 3d rotation matrix, using Python lists. We can do so by using lists of lists.
For example, the matrix
\[A= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \]
is represented by
1 | |
and the matrix
\[B= \begin{bmatrix} 1 \\ 2 \\ 3 \\ \end{bmatrix} \]
would be
1 | |
The fragments below are designed to perform operations on matrices. Your task is to match the function bodies with the correct function definitions.
A:
1 2 | |
B:
1 2 3 | |
C:
1 2 3 | |
The function bodies are given by the following
1:
1 2 | |
2:
1 | |
3:
1 | |
In scientific computing, it is a common task to take the transpose of a matrix. The transpose of a matrix \(A\), \(A^T\), is found by turning all the rows of a matrix into columns and vice versa. More formally the transpose of a matrix \(A\) is found by reflecting \(A\) over its main diagonal.
For example, the transpose of
\[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 1 & 9 \\ 8 & 0 & 1 \\ \end{bmatrix} \]
is given by
\[ A^T = \begin{bmatrix} 1 & 4 & 8 \\ 2 & 1 & 0 \\ 3 & 9 & 1 \\ \end{bmatrix} \]
Which of the following snippets of code would correctly transpose the \(30 \times 20\) matrix \(A\)?
A:
1 2 | |
B:
1 2 | |
C::
1 2 | |
D::
1 2 | |