GATE ME 2015 Set 3 | Linear Algebra Question 15 | Engineering Mathematics

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GATE ME 2015 Set 3

Numerical

-0

The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{ 4 & 2 \cr 1 & 3 \cr } } \right]$$ is ______.

Your input ____

GATE ME 2015 Set 2

MCQ (Single Correct Answer)

-0.3

At least one eigenvalue of a singular matrix is

positive

zero

negative

imaginary

GATE ME 2015 Set 1

MCQ (Single Correct Answer)

-0.3

If any two columns of a determinant $$P = \left| {\matrix{ 4 & 7 & 8 \cr 3 & 1 & 5 \cr 9 & 6 & 2 \cr } } \right|$$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?

absolute value remains unchanged but sign will change.

Both absolute valu and sign will change

Absolute value will change but sign will not change.

Both absolute value and sign will remain unchanged.

GATE ME 2014 Set 4

MCQ (Single Correct Answer)

-0.3

Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$?

$$P(Q+R)=PQ+RP$$

$${\left( {P - Q} \right)^2} = {P^2} - 2PQ + {Q^2}$$

$$\det \,\,\left( {P + Q} \right) = \det \,P + \det \,Q$$

$${\left( {P + Q} \right)^2} = {P^2} + PQ + QP + {Q^2}$$

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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