Syllabus
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Homework
For Exam 1 (ultimately due by 5 February)
HW1: Systems of linear equations (recommended due date 17 January)
HW2: Row operations and augmented matrices (recommended due date 29 January)
For Exam 2 (ultimately due 4 March)
HW3: Matrix arithmetic
HW4: Transposes and inverses
HW5: Elementary matrices
HW6: Determinants
For Exam 3 (ultimately due 8 April)
HW7: Span and linear independence and basis
HW8: Rowspace and column space and nullspace
For final exam (ultimately due 27 April)
HW9: Eigenvalues and eigenvectors
HW10: Diagonalization
HW11: Linear transformations
Quizzes
For Exam 1
Quiz 1 (due 18 Jan in Blackboard) [soln]: Put the system into reduced row echelon form and interpret that form back as a system of linear equations:
$$\left\{ \begin{array}{lll}
2x&+17y&=23 \\
x&-y&=5 \\
3x&-34y&=3
\end{array}\right.$$
Quiz 2 (due 25 Jan in Blackboard) [soln]: Put the following matrix into row reduced echelon form: $\begin{bmatrix} 0&1&3 \\ -1&-3&3 \\ 1&-3&0\end{bmatrix}$.
Quiz 3 (due 29 Jan in Blackboard) [soln]: Find the rank of $\begin{bmatrix} 2&1&0 \\ 0&2&2 \\ -1&3&1 \end{bmatrix}$.
Quiz 4 (due 5 Feb in Blackboard): Use linear algebra to balance the following chemical reaction:
\[ XeF_4 + H_2O \longrightarrow Xe + HF + O_2 + XeO_3 \]
For Exam 2
Quiz 5 (due 13 February in Blackboard) [soln]: Find the inverse, if it exists, of the matrix $\begin{bmatrix} -1&4&5 \\ 3&6&-2 \\ 4&3&1 \end{bmatrix}$.
Quiz 6 (due 22 Feb in Blackboard) [soln]: Compute
\[ \mathrm{det} \left( \begin{bmatrix} 4&0&7 \\ 7&18&5 \\ 21&0&0 \end{bmatrix}\right) \]
For Exam 3
Quiz 7 (due 7 March in Blackboard) [soln]: Show independent or dependent:
\[ \left\{ \begin{bmatrix} 1\\ 1\\ 6\\ 2 \end{bmatrix}, \begin{bmatrix} 1\\ 0\\ 1\\ 1 \end{bmatrix}, \begin{bmatrix} 0\\ 0\\ 0\\ 1 \end{bmatrix}, \begin{bmatrix} 0\\ 1 \\ 1 \\ 1 \end{bmatrix} \right\}.\]
Quiz 8 (due 16 March 25 March in Blackboard) [soln]: Find a basis for $\text{row}(A)$ and $\text{col}(A)$ where $A = \begin{bmatrix} 4&2&0 \\ 1&6&7 \\ 9&1&8\end{bmatrix}$ and compute $\text{rank}(A)$.
Quiz 9 (due 26 March in Blackboard) [soln]: Find $\text{nul}(A)$ for $A=\begin{bmatrix} 3&1&0 \\ 0&1&1 \\ 4&2&-1 \end{bmatrix}$.
Quiz 10 (due 16 Apr in Blackboard) []: Suppose $T \colon \mathbb{R}^{2 \times 1} \rightarrow \mathbb{R}^{5\times 1}$ is a linear transformation and assume that $T\left(\begin{bmatrix} 1\\1 \end{bmatrix}\right)=\begin{bmatrix} 1\\0\\0\\1\\1\end{bmatrix}$ and $T\left(\begin{bmatrix} -2 \\1 \end{bmatrix} \right)=\begin{bmatrix} 0\\0\\1\\0\\1\end{bmatrix}$. Find $A$ so that for all $\vec{x}$, $T(\vec{x})=A\vec{x}$.
Exams
Exam 1
Exam 2
Exam 3
