1. Vector? I barely know her! Here we will look at some applications of built in vectorized
(a) Create a vector of 100 evenly spaced samples of the exponential function from 0 to 1.
(b) Approximate the integral using the trapezoid method (use trapz and multiply by the interval)
and rectangular method (sum over all points and multiply by the interval).
(c) Approximate the cumulative integral using the trapezoidal method (use cumtrapz ) and rectangular method (use cumsum).
(d) Approximate the derivative by taking the difference between all adjacent elements and dividing
by the time spacing. Similarly, approximate the second derivative. What are the lengths of
each derivative vector?
(e) Given the vector [0 1 2 3 4 5], create the vector [3 4 5 0 1 2] using circshift.
2. Array Foray Perform the following matrix operations.
(a) Use reshape to create a 10 × 10 matrix A where A =
1 11 … 91
2 12 … 92
10 20 … 100
(b) Use magic to create a 10×10 magic matrix B. Use B to create a matrix C which has the same
diagonal values of B and is zero elsewhere. Note: You might want to look up diag to see how
to do this elegantly.
(c) Flip the second column of B such that the column is inverted up down.
(d) Flip the matrix A from left to right.
(e) Make cSum the column-wise sum of every column of AB (normal matrix multiplication). The
result should be a row vector.
(f) Make cMean the row-wise mean of every row of AB (element-wise matrix multiplication). The
result should be a column vector.
(g) Delete the last column of A.
3. Gotta Go Fast Generate a 300 × 500 matrix with entries ai,j =
i+j+3 using the following
methods and use tic toc to time the speed of each and report the times in a table (using table
(a) Using for loops and no pre-allocation.
(b) Using for loops and pre-allocating memory with zeros.
(c) Using only elementwise matrix operations. Note: repmat and meshgrid will be useful here.