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Home Question Bank Other Archive 2024 December 17

Other Questions from Dec 17,2024

Browse the Other Q&A Archive for Dec 17,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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(ii) Given a matrix, \( M=\left(\begin{array}{cc}3 & -1 \\ -1 & 3\end{array}\right) \). (c) Find the inverse of \( M \). Hence or otherwise, (d) Find the point whose image is ( \( 5,-1 \) ) under the transformation represented by the matrix, \( M \). (e) Find the image of the line \( y=2 x+1 \) under the transformation defined by M.(2mks) 2) Sea la transformación lineal \( T: \mathbb{V} \rightarrow \mathbb{R}^{3} / M_{B B^{\prime}}(T)=\left(\begin{array}{rrr}0 & 0 & 0 \\ -1 & 2 & 0 \\ 1 & 2 & -4\end{array}\right) \) con \( B=\{u, v, w\} \subset V \) una base de \( \mathbb{V} \) y \( B^{\prime}=\{(1,1,-1),(2,-1,0),(1,0,0)\} \) base de \( \mathbb{R}^{3} \) 2.1) Calcule \( T(u-v) \). 2.2) Encuentre una expresión analítica de la imagen de \( T \). 2) Sea la transformación lineal \( T: \mathbb{V} \rightarrow \mathbb{R}^{3} / M_{B B^{\prime}}(T)=\left(\begin{array}{rrr}0 & 0 & 0 \\ -1 & 2 & 0 \\ 1 & 2 & -4\end{array}\right) \) con \( B=\{u, v, w\} \subset V \) una base de \( \mathbb{V} \) y \( B^{\prime}=\{(1,1,-1),(2,-1,0),(1,0,0)\} \) base de \( \mathbb{R}^{3} \) 2.1) Calcule \( T(u-v) \). 2.2) Encuentre una expresión analítica de la imagen de \( T \). 2) Sea la transformación lineal \( T: \mathbb{V} \rightarrow \mathbb{R}^{3} / M_{B B^{\prime}}(T)=\left(\begin{array}{rrr}0 & 0 & 0 \\ -1 & 2 & 0 \\ 1 & 2 & -4\end{array}\right) \) con \( B=\{u, v, w\} \subset V \) una base de \( \mathbb{V} \) y \( B^{\prime}=\{(1,1,-1),(2,-1,0),(1,0,0)\} \) base de \( \mathbb{R}^{3} \) 2.1) Calcule \( T(u-v) \). 2.2) Encuentre una expresión analítica de la imagen de \( T \). *) Determine los coeficientes reales \( a, b \) y \( c \) y los autovalores de la matriz: \( A=\left(\begin{array}{lll}1 & 1 & 1 \\ a & b & c \\ 1 & 1 & 1\end{array}\right) \) si se sabe que \( (1,1,1),(1,0,-1) \) y \( (1,-1,0) \) son sus autovectores. Find the power. Write the answer in rectangular form. \( (-3+3 i \sqrt{3})^{5} \) \( (-3+3 i \sqrt{3})^{5}=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in the form a + bi.) What do we call the liquid that is released from a landfill? Aquiferous water Leachate Let \( A=\left[\begin{array}{ccc}0 & 2 & 2 \\ 0 & -2 & -2 \\ 0 & 4 & 4\end{array}\right] \) (a) Find the dimension of ker \( A \) and give \( a \) basis. Dimension: Let \( A=\left[\begin{array}{ccc}0 & -3 & 3 \\ 0 & 3 & -3 \\ 0 & 0 & 0\end{array}\right] \), (d) Find the dimension of ker A and give a basis. Dimensions? Find all values of \( \mu \) if \( \rho(A)=3 \), where (Hint change row \( R_{34} \) ) \( A=\left[\begin{array}{rrrr}\mu & -1 & 0 & 0 \\ 0 & \mu & -1 & 0 \\ -6 & 11 & -6 & 1 \\ 0 & 0 & \mu & -1\end{array}\right] \)
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