GATE ME 2012 | Linear Algebra Question 18 | Engineering Mathematics

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

GATE ME 2010

MCQ (Single Correct Answer)

-0.3

One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 & 2 \cr 1 & 3 \cr } } \right]$$ is

$$\left[ {\matrix{ 2 \cr { - 1} \cr } } \right]$$

$$\left[ {\matrix{ 2 \cr 1 \cr } } \right]$$

$$\left[ {\matrix{ 4 \cr 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]$$

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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 Bearings Design of Brakes and Clutches Design of Spur Gears Fatigue Strength

Strength of Materials

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

Heat Transfer

Conduction Fin Design and Transient Heat Conduction Convection Radiation Heat Exchangers

Production Engineering

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

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

Vibrations Gears and Gear Trains Flywheel Analysis of Plane Mechanisms

Engineering Mathematics

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

Fluid Mechanics

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

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

Verbal Ability Numerical Ability