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characteristic equation

GATE Civil Engineering · Differential Equations (CE) · 2001-2025

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11
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B. S. Grewal — Higher Engineering Mathematics

Linear algebra, calculus, probability, numerical methods

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2025 PYQ

Pick the CORRECT eigen value(s) of the matrix $[\mathrm{A}]$ from the following choices. $$ [A]=\left[\begin{array}{ll} 6 & 8 \\ 4 & 2 \end{array}\right] $$

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2024 PYQ

What are the eigenvalues of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix}$ ?

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2023 PYQ

The solution of the differential equation $\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0$ is expressed as 𝑦 = 𝐶 1 𝑒 2.5𝑥 + 𝐶 2 𝑒 𝛼𝑥 + 𝐶 3 𝑒 𝛽𝑥 , wher...

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2018 Q1

Consider the following simultaneous equations (with c₁ and c₂ being constants): 3 x₁ + 2 x₂ = c₁ 4 x₁ + x₂ = c₂ The characteristic equation for these simultaneous equations is

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2017 PYQ

Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$ The characteristic equation...

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2012 PYQ

The eigen values of matrix $$\left[ {\matrix{ 9 & 5 \cr 5 & 8 \cr } } \right]$$ are

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2010 PYQ

The solution to the ordinary differential equation $${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} - 6y = 0\,\,\,$$ is

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2008 PYQ

The eigenvalues of the matrix $$\left[ P \right] = \left[ {\matrix{ 4 & 5 \cr 2 & { - 5} \cr } } \right]$$ are

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2004 PYQ

The eigen values of the matrix $$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$ are

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2002 PYQ

Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} & 4 \cr 4 & { - 1} \cr } } \right]$$

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2001 PYQ

The eigen values of the matrix $$\left[ {\matrix{ 5 & 3 \cr 2 & 9 \cr } } \right]$$ are

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