Other Math Archive: Questions from October 16, 2022
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4. Find \( y \) ' when: (a) \( y=e^{-x-5} \) (b) \( y=\ln \left(e^{-x}+3\right) \) (c) \( x y^{3}-x^{3} y=2 x \)1 answer -
Prove the following set inclusion: \[ \bigcup_{j=1}^{\infty}\left\{(x, y) \in \mathbb{R}^{2}: x+y=j\right\} \subseteq \bigcap_{k=1}^{\infty}\left\{(x, y) \in \mathbb{R}^{2}: x+y>-k\right\} \]2 answers -
Q3. [10 marks] Solve Bernoulli's equation \[ \frac{d y}{d x}+\frac{y}{x-1}=4(x-1) \sqrt{y} \] (flnswer: \( \left.\sqrt{y}=\frac{4}{5}(x-1)^{x}+\frac{c}{\sqrt{x-1}}\right) \)1 answer -
Which of the following characteristic spaces correspond to the eigenvalues of eigenvectors of the matrix: NOTE: Adhere strictly to the nomenclature used to define characteristic spaces.
Cuál o cuáles de los siguientes espacios característicos se corresponden con los autovalores de autovectores de a matriz: \[ \left[\begin{array}{lll} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{array}0 answers -
Given the eigenvalue: Identify which of the following matrices it belongs to:
Dado el valor propio: \[ \lambda=5 \] Identifique a cuál o cuáles de las matrices siguientes pretenece: \[ \left(\begin{array}{ccc} -10 & -71 & -19 \\ 3 & 34 & 9 \\ -1 & -61 & -16 \end{array}\right)0 answers -
Given the matrix: Determine the algebraic and geometric multiplicity for each of the eigenvalues associated with the matrix. INDICATIONS: Sort the eigenvalues in ascending order. Sele
Dada la matriz: \[ \left(\begin{array}{ccc} 13 & 3 & 1 \\ -56 & -13 & -4 \\ -14 & -3 & -2 \end{array}\right) \] Determine la multiplicidad algebraica y geométrica para cada uno de los autovalores aso2 answers -
Given the matrix: What geometric transformation does it cause on the vectors in R2?
Dada la matriz: \[ \left(\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right) \] ¿Qué transformación geométrica provoca sobre los vectores en \( \mathrm{R}^{2} \) ? Reflexión en el eje \( y \). R0 answers -
Given the matrix: Identify which of the following matrices it is similar to:
Dada la matriz: \[ D=\left(\begin{array}{lll} 1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2 \end{array}\right) \] Identifique con cuál o cuáles de las matrices siguientes es semejante: \[ \left(\begin{array}{0 answers