Topic
Q:
Explain the difference between exponential growth and exponential decay.
Q:
Нзобразить корни 2 степени из \( \frac{1}{2}+i \cdot \frac{\sqrt{3}}{2} \) на комплексной плоскости.
Q:
14. Which of the following statement is false?
A. \( \{\emptyset\} \in\{0,\{\varnothing\}\} \)
B. \( \emptyset \subseteq\} \)
C. \( \{\emptyset\}=\{ \} \)
D. \( \emptyset \subseteq\{0,\{\varnothing\}\} \)
Q:
A computer technician charges a fixed amount for a repair, plus an additiona
What is the meaning of the initial amount for the equation?
A. It means the technician charges \( \$ 45 \) per hour for the repair.
B. It means the technician charges a fixed amount of \( \$ 45 \) for the repair.
C. It means the technician charges a fixed amount of \( \$ 75 \) for the repair,
D. It means the technician charges \( \$ 75 \) per hour for the repair.
Q:
Which is an advantage of roottop gardens over traditional gardens?
A. better drainage
C. more soil in which plants can spread out
D. cooler growing season
Q:
\( A=\left[\begin{array}{cc}-6 & 3 \\ -2 & -1\end{array}\right] \) has the following eigenpairs.
\[ \left(r_{1}=-4, \mathbf{c}_{1}=\left[\begin{array}{l}3 \\ 2\end{array}\right]\right)\left(r_{2}=-3, \mathbf{c}_{2}=\left[\begin{array}{l}1 \\ 1\end{array}\right]\right) \]
Find the general solution to the following system of differential equations.
\[ \begin{array}{l}y_{1}^{\prime}=-6 y_{1}+3 y_{2} \\ y_{2}^{\prime}=-2 y_{1}-y_{2}\end{array} \]
\[ \begin{array}{l}\mathbf{y}=k_{1}\left[\begin{array}{r}\square \\ \square\end{array}\right] e^{\square} t+k_{2}\left[\begin{array}{l}\square \\ \square\end{array}\right]\end{array} \]
Q:
Find the pseudoinverse of \( \left[\begin{array}{ll}3 & 1 \\ 2 & 1\end{array}\right] \)
Q:
Determine which formula(s) can be used to find the pseudoinverse of \( A=\left[\begin{array}{ccc}1 & 1 & 3 \\ 3 & 3 & 9 \\ 5 & 5 & 15\end{array}\right] \).
\( A^{+}=A^{T}\left(A A^{T}\right)^{-1} \)
\( A^{+}=\left(A^{T} A\right)^{-1} A^{T} \)
\( A^{+}=\lim _{\alpha \rightarrow 0}\left(A^{T} A+\alpha^{2} I\right)^{-1} A^{T} \)
Q:
Let \( A=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right] \) be a \( 2 \times 2 \) matrix. Let \( f_{A}: R^{2} \times R^{2} \rightarrow R \) defined by
\( f_{A}(X, Y)={ }^{t} X A Y \) is a symmetric bilinear form where \( X, Y \) are column
vectors in \( R^{2} \). Then find the matrix of \( f_{A} \) with respect to the basis (i)
\( \{(1,0),(0,1)\} \) and (ii) \( \{(1,1),(1,-1)\} \).
Q:
Let \( A=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right] \) be a \( 2 \times 2 \) matrix. Let \( f_{A}: R^{2} \times R^{2} \rightarrow R \) defined by
\( f_{A}(X, Y)=T A Y \) is a symmetric bilinear form where \( X, Y \) are column
vectors in \( R^{2} \). Then find the matrix of \( f_{A} \) with respect to the basis (i)
\( \{(1,0),(0,1)\} \) and (ii) \( \{(1,1),(1,-1)\} \).
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