1
GATE CE 2005
+1
-0.3
Consider a non-homogeneous system of linear equations represents mathematically an over determined system. Such a system will be
A
Consistent having a unique solution
B
Consistent having many solutions.
C
Inconsistent having a unique solution.
D
none
2
GATE CE 2005
+1
-0.3
Consider the following system of equations in three real variable $${x_1},$$ $${x_2}$$ and $${x_3}:$$ $$2{x_1} - {x_2} + 3{x_3} = 1$$$$$3{x_1} + 2{x_2} + 5{x_3} = 2$$$ $$- {x_1} + 4{x_2} + {x_3} = 3$$\$

This system of equations has

A
no solution
B
a unique solution
C
more then one but a finite number of solutions.
D
an infinite number of solutions.
3
GATE CE 2005
+1
-0.3
Consider the matrices $$\,{X_{4x3,}}\,\,{Y_{4x3}}$$ $$\,\,{P_{2x3}}.$$ The order of $$\,{\left[ {P{{\left( {{X^T}Y} \right)}^{ - 1}}{P^T}} \right]^T}$$ will be
A
$$2 \times 2$$
B
$$3 \times 3$$
C
$$\,4 \times 3\,$$
D
$$\,3 \times 4\,$$
4
GATE CE 2005
+1
-0.3
Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda$$ is a scalar. Let $$\left( {{\lambda _i},\,\,{X_i}} \right)$$ be an eigen value and its corresponding eigen vector for real matrix $$A$$. Let $${{\rm I}_{nxn}}$$ be unit matrix. Which one of the following statement is not correct?
A
For a homogeneous $$nxn$$ system of linear equations $$\left( {A - \lambda {\rm I}} \right)X = 0,$$ having a non trivial solution, the rank of $$\left( {A - \lambda {\rm I}} \right)$$ is less then $$n.$$
B
For matrix $${A^m},$$ $$m$$ being a positive integer, $$\left( {{\lambda _i}^m,\,{X_i}^m} \right)$$ will be eigen pair for all $$i.$$
C
If $${A^T} = {A^{ - 1}}$$ then $$\left| {{\lambda _i}} \right| = 1$$ for all $$i.$$
D
If $${A^T} = A$$ then $${{\lambda _i}}$$ are real for all $$i.$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination