GATE CE 2022 Set 2 | Linear Algebra Question 11 | Engineering Mathematics

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GATE CE 2022 Set 2

MCQ (More than One Correct Answer)

-0.33

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 $${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.

GATE CE 2022 Set 1

MCQ (More than One Correct Answer)

-0.33

The matrix M is defined as

$$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$

and has eigenvalues 5 and $$-$$2. The matrix Q is formed as

Q = M³ $$-$$ 4M² $$-$$ 2M

Which of the following is/are the eigenvalue(s) of matrix Q?

$$-$$20

$$-$$30

GATE CE 2022 Set 1

MCQ (Single Correct Answer)

-0.33

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinate system about the positive x-axis are

(1, 0, $$\sqrt 2 $$)

(1, 0, $$-$$$$\sqrt 2 $$)

($$-$$1, 0, $$\sqrt 2 $$)

($$-$$1, 0, $$-$$$$\sqrt 2 $$)

GATE CE 2017 Set 1

MCQ (Single Correct Answer)

-0.3

The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?

$$PQ = {\rm I}\,\,\,but\,\,\,QP \ne {\rm I}$$

$$QP = {\rm I}\,\,\,but\,\,\,PQ \ne {\rm I}$$

$$PQ = {\rm I}\,\,\,and\,\,\,QP = {\rm I}$$

$$PQ - QP = {\rm I}$$

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GATE CE Subjects

Engineering Mechanics

Work Energy Principle and Impulse Momentum Equation Equilibrium of Force Systems

Strength of Materials Or Solid Mechanics

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

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

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Reinforced Cement Concrete

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

Steel Structures

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

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

Hydrology

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

Irrigation

Water Requirement of Crops Gravity Dams and Spillways

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

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

Transportation Engineering

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

Engineering Mathematics

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

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability