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--- gibson:teaching:spring-2015:math445:lab2 [2015/01/28 10:55]
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 ====== Math 445 lab 2: Vectors and Matrices ======
-**1**
+----
+**Problem 1.** Creation of vectors. Show how to create the following vectors in Matlab three different ways,
+using square brackets, ''linspace,'' and colon syntax.
+**(a)** The row vector
+\begin{eqnarray*}
+x = (1, 3, 5, 7, 9)
+\end{eqnarray*}
+**(b)** The column vector
+\begin{eqnarray*}
+x = \left(\begin{array}{c}
+\\ 1 \\ -3 \\ -7 \\ -11
+    \end{array}\right)
+\end{eqnarray*}
+**%%(c)%%** The row vector
+\begin{eqnarray*}
+x = (1, 3, 9, 27, 81)
+\end{eqnarray*}
+**(d)** A column vector $x$ of 100 evenly spaced values between -1 and 13, including those endpoints. Listing
+out all the elements with square bracket syntax would be very tedious and error-prone, so just show how to
+do this with ''linspace'' and colon syntax.
+----
+**Problem 2:** Extracting and assigning subvectors. Given the $x$ vector of problem 1d,
+**(a)** What is the value of the 73th element of $x$?
+**(b)** Assign every seventh element of $x$ into the vector $v$. How many elements does $v$ have?
+What is the value of $v$'s second-to-last element?
+**%%(c)%%** Set elements 21 through 29 of $x$ to the values of elements 34 through 42.
+**(d)** Set elements 21 through 29 of $x$ to the values of elements 42 through 34 (same as before but backwards!)
+**(e)** Modify the $x$ vector so that every other element between 21 through 31 is zero.
+----
+**Problem 3.** Creation of matrices, extracting and assigning elements and subvectors.
+**(a)** Create the matrix A
+\begin{eqnarray*}
+A = \left[ \begin{array}{rrr} 3 & 7 & 2 \\ -2 & 4 & 6 \\ 5 & 1 & 0 \end{array} \right]
+\end{eqnarray*}
+**(b)** Change $A_{2,3}$ to 7.
+**%%(c)%%** Assign the third column of A to the variable v.
+**(d)** Change the first row of A to (8, 1, 4).
+**(e)** Change A so that all the values in the second column are doubled. Do this in one line of Matlab code
+that extracts the second column, multiplies it by 2, and then assigns it back into the second column.
+----
+**Problem 4. Extracting and assigning submatrices.**
+**(a)** Create a $5 \times 5$ matrix A of zeros.
+**(b)** Assign the upper-left $2 \times 3$ submatrix of A to
+\begin{eqnarray*}
+\left[ \begin{array}{rrr} 1 & -4 & 3 \\  6 & 2 & 1 \end{array} \right]
+\end{eqnarray*}
+**%%(c)%%** Assign ones to the bottom-right $3 \times 3$ submatrix of A.
+**(d)** Set the third column of A to a normally-distributed random vector.
+**(e)** What is the fourth row of $A$?
+**(f)** What is the central $3 \times 3$ submatrix of $A$?

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