Linear Algebra: UNIT III: Inner Product Spaces
Inner Product Spaces : Multiple Choice Questions and Answers
Linear Algebra
Linear Algebra: UNIT III: Inner Product Spaces: Multiple Choice Questions and Answers
INNER
PRODUCT SPACES
MULTIPLE CHOICE
QUESTION AND ANSWERS
1. The process of
multiplying a non−zero vector by the reciprocal of its length is called
(A)
Norm
(B)
Inner product
(C)
Normalizing
(D)
Vector space
2. Let V be an inner
product space. A subset of V is an orthonormal basis for V if, it is an ordered
basis is
(A)
Orthonormal
(B)
Orthogonal
(C)
Inner product
(D)
Ordered pair
3. Let V be an inner
product space over F, for all x, y ∈
V and c ∈
F. Then the Cauchy−Schwarz inequality is
(A)
|| cx || = c || x ||
(B)
|| x + y || = 0
(C)
|| x+y|| = || x || + || y ||
(D) |
<x+y> | ≤ || x || + || y ||
4. Let V be an inner
product space over F, for all x, y ∈
V and c ∈
F. Then the triangle inequality is
(A)
||cx||=c||x||
(B)
||x+y||=0
(C)
||x+y||≤ || x || + || y ||
(D)
||x|| ||y||=0
5. Let V be the vector
space of polynomial with inner product given by <f, g> = 0ʃ1 f(t) g(t) dt. Define f(t) = t +2 and g(t)=t2−2t−3
then the value of <f, g> is
(A)
37/4
(B) −37/4
(C)
4/37
(D)
−4/37
6. Let V be the vector
space of polynomial with inner product given by <f,g> = 0ʃ1
f(t)g(t) dt. Define f(t) = t=t+2 and g(t) = t2 −
2t−3 then the value of <f.f> is
(A) 19/3
(B)
−19/3
(C)
3/19
(D)
−3/19
7. Let f(t) = t and g(t)= et. Then
the value of ||f|| in C[0, 1] is
(A)
1/3
(B) 1/√3
(c) −1/3
(D)
−1/√3
8. Let f(t) = t and g(t)=et, then
the value of || g || in C [0, 1] is
(A) √[(e2‒1)/2]
(B)
√[2/(e2‒1)]
(C)
√[(e2‒1)/3]
(D)
√[3/(e2‒1)]
9. Let V=C3
with inner product <x, y> = x1
1+x22+x33 where x= (x1, x2,
x3) and y = (y1, y2, y3). Let x =
(2, 1+ i, i), y=(2−i, 2, 1+2i) then the value of <x, y> is
(A) 8+5i
(B)
8−5i
(C)
8i +5
(D)
8i−5
10. For the same
problem in 9, the value of || x || is
(A)
√6
(B) √7
(C)
√8
(D)
√5
Linear Algebra: UNIT III: Inner Product Spaces : Tag: maths, mathematics : Linear Algebra - Inner Product Spaces : Multiple Choice Questions and Answers
Linear Algebra: UNIT III: Inner Product Spaces
Under Subject
Linear Algebra
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