GATE ME 2013 | Linear Algebra Question 23 | Engineering Mathematics

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GATE ME 2013

MCQ (Single Correct Answer)

-0.3

The eigen values of a symmetric matrix are all

complex with non-zero positive imaginary part.

complex with non-zero negative imaginary part.

real

pure imaginary

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as

$$\left( {\matrix{ {{1 \over 2}} \cr {{{\sqrt 3 } \over 2}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over {\sqrt 2 }}} \cr {{{ - 1} \over {\sqrt 2 }}} \cr } } \right)$$

$$\left( {\matrix{ {{3 \over {\sqrt {10} }}} \cr {{{ - 1} \over {\sqrt {10} }}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over 5}} \cr {{2 \over {\sqrt 5 }}} \cr } } \right)$$

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

Eigen values of a real symmetric matrix are always

positive

negative

real

$$162.$$ $$\left[ {\rm A} \right]$$ is a square

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

Consider the following system of equations
$$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0.$$
This system has

a unique solution

no solution

infinite number of solutions

five solutions

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GATE ME Subjects

Engineering Mechanics

Engineering Mechanics Static and Dynamics

Machine Design

Bolted Riveted and Welded Joints Design For Static Loading Design of Brakes and Clutches Design of Spur Gears Design of Bearings Fatigue Strength

Strength of Materials

Springs Pure Bending Stresses In Beams Simple Stress and Strain Complex Stresses Moment of Inertia Deflection of Beams Shear Force and Bending Moment Torsion Thin Cylinders Columns and Struts Strain Energy Method

Heat Transfer

Conduction Fin Design and Transient Heat Conduction Convection Radiation Heat Exchangers

Production Engineering

Metrology and Inspection Sheet Metal Forming Processes Welding Process Metal Forming Metal Cutting Advance Machine Tools Machining Casting

Industrial Engineering

Queuing Production Planning and Control Line Balancing Forecasting Pert and Cpm Inventory Control Transportation Scheduling Linear Programming Assignment

Turbo Machinery

Theory of Machines

Analysis of Plane Mechanisms Gears and Gear Trains Vibrations Flywheel

Engineering Mathematics

Linear Algebra Calculus Vector Calculus Probability and Statistics Differential Equations Complex Variable Transform Theory Numerical Methods

Fluid Mechanics

Fluid Properties Fluid Statics Boundary Layer Turbulent Flow Laminar Flow Fluid Dynamics Fluid Kinematics

Thermodynamics

Calculation of Work and Heat Entropy and Irreversibility Properties of Pure Substances Basic Concepts and Zeroth Law First Law of Thermodynamics Rankine Cycle Availability Second Law of Thermodynamics

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability