#books q

amit166 asked Nov 13, 2018

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rajveer43 asked Jan 11

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GATE 2016 | MATHS | Q-48
Let $ M= \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} $ and $ e^M = Id + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \frac{M^4}{4!} + \ldots $. If $ e^M = [b_{ij}]$. then \[\frac{1}{e} \sum_{i=1}^{3} \sum_{j=1}^{3} b_{ij} \] is equal to ________________________

Let $ M= \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} $ and $ e^M = Id + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \frac{M^4}{4!} + \ldots $. If \( e...

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GATE 2016 | MATHS | Q-12
Consider the following statements P and Q: (P) : If $ M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} $, then M is singular. (Q) : Let S be a diagonalizable matrix. If T is a matrix such that \( ... ), then T is diagonalizable. Which of the above statements hold TRUE? (A) both P and Q (B) only P (C) only Q (D) Neither P nor Q

Consider the following statements P and Q:(P) : If $ M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} $, then M is singular.(Q) : Let S be a diagon...

rajveer43

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GATE 2016 | MATHS | Q-14
Consider a real vector space $ V $ of dimension $ n $ and a non-zero linear transformation $ T: \mathbb{V} \rightarrow \mathbb{V} $. If $ \text{dim}(T) < n $ and $T^2 = \lambda T$, for some $ \lambda \in \mathbb{R} \backslash \{0\} $, then which ... 0 \) for all $ X \in \mathbb{W} $ (C) $ T $ is invertible (D) $ \lambda$ is the only eigenvalue of $ T $

Consider a real vector space $ V $ of dimension $ n $ and a non-zero linear transformation $ T: \mathbb{V} \rightarrow \mathbb{V} $. If $ \text{dim}(T) < n $ and ...

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GATE 2018 | MATHS | Q-55
Let $ A $ be a $3 \times 3$ matrix with real entries. If three solutions of the linear system of differential equations $\dot{x}(t) = Ax(t)$ are given by \[ \begin{bmatrix} e^t - e^{2t} \\ -e^{t} + e^{2t} \\ e^t + e^{2t} \end{bmatrix}, \begin{bmatrix} ... \\ e^{-t} - 2e^t \\ -e^{-t} + 2e^t \end{bmatrix}, \] then the sum of the diagonal entries of $ A $ is equal to

Let $ A $ be a $3 \times 3$ matrix with real entries. If three solutions of the linear system of differential equations $\dot{x}(t) = Ax(t)$ are given by\[\begin{bm...

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