GATE CE 2023 Set 1 | Linear Algebra Question 7 | Engineering Mathematics

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GATE CE 2023 Set 1

MCQ (More than One Correct Answer)

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If M is an arbitrary real n × n matrix, then which of the following matrices will have non-negative eigenvalues?

MMT

MTM

(MT)2

GATE CE 2022 Set 2

MCQ (More than One Correct Answer)

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Let y be a non-zero vector of size 2022 $$\times$$ 1. Which of the following statements is/are TRUE?

yy^T is symmetric matrix

yy^T is invertible

yy^T has a rank of 2022

y^Ty is an eigen value of yy^T.

GATE CE 2022 Set 2

Numerical

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The components of pure shear strain in a sheared are given in the matrix form:

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

Here, Trace ($$\varepsilon $$) = 0. Given, P = Trace ($$\varepsilon$$⁸) and Q = Trace ($$\varepsilon $$¹¹).

The numerical value of (P + Q) is ___________. (in integer)

Your input ____

GATE CE 2022 Set 2

MCQ (More than One Correct Answer)

-0

P and Q are two square matrices of the same order. Which of the following statements is/are correct?

If P and Q are invertible, then$${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.

If P and Q are invertible, then $${[PQ]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.

If P and Q are invertible, then $${[QP]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.

If P and Q are not invertible, then $${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.

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GATE CE Subjects

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Geomatics Engineering Or Surveying

Levelling Traversing Theodolites and Plane Table Surveying Measurement of Area, Volume and Theory of Errors and Survey Adjustment Field Astronomy and Photogrammetric Surveying Basics of GIS, GPS and Remote Sensing Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey

Engineering Mechanics

Equilibrium of Force Systems Work Energy Principle and Impulse Momentum Equation

Hydrology

Precipitation and Frequency of Rainfall Data Evaporation and Transpiration Infiltration Hydrograph Flood Estimation and Flood Routing

Transportation Engineering

Highway Devolopment and Planning Highway Geometric Design Traffic Engineering Highway Materials Pavement Design Railway, Runway and Taxiway Design

Strength of Materials Or Solid Mechanics

Pure Bending Shear Stress In Beams Simple Stresses Complex Stress Centroid and Moment of Inertia Torsion Shear Force and Bending Moment Deflection of Beams Thin Cylinder Strain Energy Method Columns and Struts Propped Cantilever Beam

Reinforced Cement Concrete

Singly Reinforced Sections Workmenship and Fundamentals Doubly Reinforced Sections Flanged Beams Limit State of Collapse Shear Limit State of Collapse Torsion Limit State of Collapse Compression Footings Bond Limit State of Serviceability Prestressed Concrete Slabs

Steel Structures

Eccentric Connections Plate Girder Tension Members Welded Connections Materials and Specifications Riveted Joints and Bolted Joints Beams Compression Members

Irrigation

Water Requirement of Crops Gravity Dams and Spillways

Environmental Engineering

Sources and Coveyances Water Quality Control of Water Treatment of Water Water Demand Waste Water Characteristics Treatment of Sewage Disposal of Sewage Effluent Solid Waste Management Air Pollution Noise Pollution

Engineering Mathematics

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

Structural Analysis

Energy Principle Truss Stability and Static Indeterminacy Methods of Analysis Indeterminacy Arches and Cable Slope Deflection Method Matrix Method Moment Distribution Method Influence Line Diagram Plastic Analysis

Geotechnical Engineering

Origin of Soils Definitions and Properties of Soils Classification of Soils and Clay Mineralogy Effective Stress and Permeability Seepage Analysis Compaction of Soil Compressibility and Consolidation Shear Strength of Soil Stress Distribution of Soil Retaining Wall and Earth Pressure Stability of Slopes Shallow Foundation Pile Foundation Soil Stabilization

Fluid Mechanics and Hydraulic Machines

Fluid Pressure and Measurement Fluid Dynamics Boundary Layer Theory Drag and Lift Flow Through Pipes Open Channel Flow Hydraulic Machines Properties of Fluids Fluid Statics

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability