Login
Premium
Home Question Bank Other Archive 2024 December 21

Other Questions from Dec 21,2024

Browse the Other Q&A Archive for Dec 21,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

error msg
\( A=\left[\begin{array}{cc}-6 & 3 \\ -2 & -1\end{array}\right] \) 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. \[ \begin{array}{l}y_{1}^{\prime}=-6 y_{1}+3 y_{2} \\ y_{2}^{\prime}=-2 y_{1}-y_{2}\end{array} \] \[ \begin{array}{l}\mathbf{y}=k_{1}\left[\begin{array}{r}\square \\ \square\end{array}\right] e^{\square} t+k_{2}\left[\begin{array}{l}\square \\ \square\end{array}\right]\end{array} \] Find the pseudoinverse of \( \left[\begin{array}{ll}3 & 1 \\ 2 & 1\end{array}\right] \) Determine which formula(s) can be used to find the pseudoinverse of \( A=\left[\begin{array}{ccc}1 & 1 & 3 \\ 3 & 3 & 9 \\ 5 & 5 & 15\end{array}\right] \). \( A^{+}=A^{T}\left(A A^{T}\right)^{-1} \) \( A^{+}=\left(A^{T} A\right)^{-1} A^{T} \) \( A^{+}=\lim _{\alpha \rightarrow 0}\left(A^{T} A+\alpha^{2} I\right)^{-1} A^{T} \) 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) \( \{(1,1),(1,-1)\} \). 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) \( \{(1,1),(1,-1)\} \). 5. 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) \( \{(1,1),(1,-1)\} \). 5. Let \( A=\left[\begin{array}{ll}1 & 3 \\ 2 & 3\end{array}\right] \) be a \( 2 \times 2 \) matrix. Let \( f_{A}: R^{2} \times R^{2} \rightarrow R \) defined by \( f_{A}(X, Y)= \) 'XAY 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 \( A=\left(\begin{array}{ccc}2 & -1 & 3 \\ 2 & -1 & 3 \\ 3 & 2 & -1\end{array}\right) \). Then the largest eigenvalue of \( A \) is \( \ldots \). 5. Find the truth value of each of the following and justify your conclusion. a. \( \phi \subseteq \phi \) b. \( \{1,2\} \subseteq\{1,2\} \) c. \( \phi \in A \) for any set A d. \( \{\phi\} \subseteq A \), for any set \( A \) e. \( 5,7 \subseteq\{5,6,7,8\} \) f. \( \phi \in\{\{\phi\}\} \) g. \( \quad \) For any set \( A, A \subset A \) h. \( \{\phi\}=\phi \) 6. For each of the following set, find its power set. a. \( \{a b\} \) b. \( \{1,1.5\} \) c. \( \{a, b\} \) d. \( \{a, 0.5, x\} \) 7. How many subsets and proper subsets do the sets that contain exactly \( 1,2,3,4,8,10 \) 20 elements have? 8. Is there a set \( A \) with exactly the following indicated property? a. Only one subset b. Only one proper subset 5.] Let \( A=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right] \) be a \( 2 \times 2 \) matrix. Let \( f_{A}: \mathbb{R}^{2} \times R^{2} \rightarrow \mathbb{R} \) defined by \( f_{A}(x, y)={ }^{t} \times A y \) is a symmetric bilinear form Where \( x, y \) are column wector in \( \mathbb{R}^{2} \). Then find the matrix of \( f_{A} \) with respect to the basis (i) \( \left.z(1,0),(0,1)\right\} \) (1) \( \alpha(1,1),(1,-1)\} \).
Prev 1 2 Next
1 2
Prev Next
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy