Exercise 11.3

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Exercise 11.3#

Question 1#

Consider the matrix:

\begin{array}{r} (\begin{array}{c} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \end{array}) \end{array}

Enter this matrix into your script and preform the following tasks:

Extract the second column.
Extract the central $2 \times 2$ block.
Find the transpose of the matrix.

Question 2#

Consider the matrix equation: $A x = B$ , where $A$ and $B$ are known matrices and $x$ is an unknown matrix. Write a program which solves this equation for $x$ , assuming $A$ is a square matrix. Test it with the following example:

\begin{array}{r} A = (\begin{array}{c} 2 & 6 \\ 8 & 3 \end{array}) and B = (\begin{array}{c} 7 \\ 3 \end{array}) which gives x = (\begin{array}{c} - 0.0714 \\ 1.1905 \end{array}) \end{array}

Bonus: Can you write a program which solves this for non-square matrices? (see numpy.linalg.lstsq).

Test it on the following example:

\begin{array}{r} A = (\begin{array}{c} 5.3 & 4.2 & 2.9 \\ 3.4 & 2.7 & 12.1 \end{array}) and B = (\begin{array}{c} 7.4 \\ 1.7 \end{array}) which gives x = (\begin{array}{c} 0.9580 \\ 0.7587 \\ - 0.2980 \end{array}) \end{array}