GATE ME 2012 | Linear Algebra Question 20 | 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 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

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 Linear Programming Assignment Pert and Cpm Inventory Control Transportation Scheduling

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

Thermodynamics

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

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability