Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev

Topic wise GATE Past Year Papers for Civil Engineering

GATE : Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev

The document Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev is a part of the GATE Course Topic wise GATE Past Year Papers for Civil Engineering.
All you need of GATE at this link: GATE

Q.1. Consider the hemispherical tank of radius 13 m as shown in the figure (not drawn to scale). What is the volume of water (in m3) when the depth of water at the centre of the tank is 6 m?    
[2019: 2 Marks, Set-ll]
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
(a) 156π
(b) 396π
(c) 468π 
(d) 78π

Ans. (b)
Solution. Volume of water
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Q.2. The inverse of the matrix Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev    
[2019: 2 Marks, Set-ll]
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Ans. (d)
Q.3. The rank of the following matrix is Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev    
[2018 : 2 Marks, Set-II]
(a) 1 
(b) 2
(c) 3 
(d) 4
Ans. (b)
Solution. 
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
► Number of non zero rows = 2
► Rank of A = 2

Q.4. The matrix Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev has    
[2018 : 2 Marks, Set-II]
(a) real eigenvalues and eigenvectors 
(b) real eigenvalues but complex eigenvectors 
(c) complex eigenvalues but real eigenvectors 
(d) complex eigenvalues and eigenvectors
Ans. (d)
Solution. 
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev

Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
 Complex Eigenvalues and complex Eigen vectors.

Q.5. Which one of the following matrices is singular?    
[2018: 1 Marks, Set-I]
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Ans. (c)
Solution. Option (a): |A| = 6 - 5 = 1
Option (b): |A| = 9 - 4 = 5
Option (c): |A| = 12-12 = 0
Option (d): |A| = 8 - 18 = -10
Hence matrix (c) is singular.

Question 1:For the given orthogonal matrix Q,    [2018: 1 Marks, Set-I]
Linear Algebra (Part - 1)
The inverse is


Q.7. If  A = Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRevand B = Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev ABT is equal to    
[2017 : 2 Marks, Set-II]
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Ans. (a)
Solution. 
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev

Q.8. Consider the following simultaneous equations (with c1 and c2 being constants):    
[2017 : 1 Mark, Set-II]
3x1 + 2x2 = c1 
4x1 + x2 = c2 
The characteristics equation for these simultaneous equations is 
(a) λ2 - 4λ - 5 = 0 
(b) λ2 - 4λ + 5 = 0 
(c) λ2 + 4λ - 5 = 0 
(d) λ2 + 4λ + 5 = 0 
Ans. (a)
Solution. 
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev
|A - λI| = 0
(3 - λ) (1 - λ) - 8 = 0
3 - 4λ + λ2 - 8 = 0
λ2 - 4λ - 5 = 0

Question 2:Consider the matrix Linear Algebra (Part - 1) Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?    [2017: 2 Marks, Set-I]


Q.10. The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?  [2017: 1 Mark, Set-I]
(a) PQ = I but QP ≠ I 
(b) QP = I but PQ ≠ I 
(c) PQ = I and QP = I 
(d) PQ = QP = I
Ans. (c)
Solution. Given that P is inverse of Q.
► P = Q-1   
► PQ = Q-1Q,  QP = QQ-1
► PQ = I , QP = I
∴ PQ = QP = I

Question 3:Consider the following linear system.    [2016 : 2 Marks, Set-Il]
x + 2y - 3z = a 
2x + 3y + 3x = b 
5x + 9y - 6z = c
This system is consistent if a, b and c satisfy the equation 

Question 4:If the entries in each column of a square matrix M add up to 1, then an eigen value of M is [2016 : 1 Mark, Set - I]

Question 5:The two Eigenvalues of the matrix Linear Algebra (Part - 1) have a ratio of 3 : 1 for p = 2. What is another value of p for which the Eigenvalues have the same ratio of 3 : 1?   
[2015: 2 Marks, Set-II]

Question 6:Let A =Linear Algebra (Part - 1) with n > 3 and aij = i.j. The rank of A is    [2015 : 1 Mark, Set-II]

Question 7:The smallest and largest Eigen values of the following matrix are Linear Algebra (Part - 1)    [2015 : 2 Marks, Set-I]

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

MCQs

,

study material

,

Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev

,

Viva Questions

,

past year papers

,

video lectures

,

Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev

,

ppt

,

Exam

,

Summary

,

Semester Notes

,

mock tests for examination

,

Sample Paper

,

Extra Questions

,

Free

,

Linear Algebra (Part - 1) Civil Engineering (CE) Notes | EduRev

,

Important questions

,

pdf

,

Previous Year Questions with Solutions

,

practice quizzes

,

shortcuts and tricks

,

Objective type Questions

;