GATE CE 2022 Set 1 | Linear Algebra Question 17 | Engineering Mathematics

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 2

MCQ (Single Correct Answer)

-0.3

Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$

The characteristic equation for these simultaneous equation is

$${\lambda ^2} - 4\lambda - 5 = 0$$

$${\lambda ^2} 4\lambda + 5 = 0$$

$${\lambda ^2} + 4\lambda - 5 = 0$$

$${\lambda ^2} + 4\lambda + 5 = 0$$

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?

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

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

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

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

GATE CE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

If the entries in each column of a square matrix $$M$$ add up to $$1$$, then an eigenvalue of $$M$$ is

$$4$$

$$3$$

$$2$$

$$1$$

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GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Hydrology

Irrigation

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude