GTU Engineering 1st Year MCQ | Vector Calculus and Linear Algebra-2110015 Winter 2015 Sem-1

Vector Calculus and Linear Algebra (2110015)
Winter 2015 Sem-1

MCQ(s) of Vector Calculus and Linear Algebra (2110015) - Winter 2015 Sem-1

- Q. 1 $E i g e n v a l u e s o f A^{- 1} & A^{T} a r e s a m e i f m a t r i x A i s$
- (A) Symmetric
  
  (B) Orthogonal
- (C) Skew symmetric
  
  (D) None of these
- Answer
  
  (B) Orthogonal
- Q. 2 Rank of 4×4 invertible matrix is
- (A) 1
  
  (B) 2
- (C) 3
  
  (D) 4
- Answer
  
  (D) 4
- Q. 3 $F i s s o l e n o i d a l v e c t o r, I f d i v (F) i s$
- (A) $F$
  
  (B) 1
- (C) 0
  
  (D) -1
- Answer
  
  (C) 0
- Q. 4 Let A be a Hermition matrix, then A is
- (A) $A^{*}$
  
  (B) $A$
- (C) $A^{T}$
  
  (D) $- A^{*}$
- Answer
  
  (A) $A^{*}$
- Q. 5 $I f A = [\begin{matrix} 1 & 0 \\ 2 & - 1 \end{matrix}] t h e n e i g e n v a l u e s o f A^{3} a r e$
- (A) 1,-1
  
  (B) 0,2
- (C) 1,1
  
  (D) 0,8
- Answer
  
  (A) 1,-1
- Q. 6 $W h i c h s e t f r o m S_{1} = {a_{0} + a_{1} x + a_{2} x^{2} / a_{0} = 0} a n d S_{2} = {a_{0} + a_{1} x + a_{2} x^{2} / a_{0} \neq 0} i s s u b s p a c e o f P_{2} ?$
- (A) $s_{2}$
  
  (B) $s_{1}$
- (C) $s_{1} & s_{2}$
  
  (D) None of these
- Answer
  
  (B) $s_{1}$
- Q. 7 For which value of k vectors u=(2, 1, 3) and v=(1, 7, k) are orthogonal?
- (A) -3
  
  (B) -1
- (C) 0
  
  (D) 2
- Answer
  
  (A) -3
- Q. 8 $L e t T : R^{3} \to R^{3} b e o n e t o o n e l i n e a r t r a n s f o r m a t i o n t h e n t h e d i m e n s i o n o f k e r (T) i s$
- (A) 0
  
  (B) 1
- (C) 2
  
  (D) 3
- Answer
  
  (A) 0
- Q. 9 The column vector of an orthogonal matrix are
- (A) orthogonal
  
  (B) orthonormal
- (C) dependent
  
  (D) none of these
- Answer
  
  (B) orthonormal
- Q. 10 $I f r = x i + y j + z k t h e n d i v (r) i s$
- (A) r
  
  (B) 0
- (C) 1
  
  (D) 3
- Answer
  
  (D) 3
- Q. 11 The number of solution of the system of equation AX=0 (where A is a singular matrix) is
- (A) 0
  
  (B) 1
- (C) 2
  
  (D) infinite
- Answer
  
  (D) infinite
- Q. 12 If the value of line integral does not depend on path C then F is
- (A) solenoidal
  
  (B) imcompressible
- (C) irrotational
  
  (D) none of these
- Answer
  
  (C) irrotational
- Q. 13 $A C a y l e y - H a m i l t o n t h e o r e m h o l d f o r______m a t r i c e s o n l y$
- (A) singular
  
  (B) all square
- (C) null
  
  (D) a few rectangular
- Answer
  
  (B) all square
- Q. 14 $I f A = [\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}] t h e n r a n k o f m a t r i x A i s$
- (A) 1
  
  (B) 0
- (C) 2
  
  (D) 4
- Answer
  
  (A) 1