(2.) Let V be the vector space of M1x2(C) over R. (a.) Give a basis for V. (b.) Let W = { { 1] z €R. By using the definition of subspace, deter- mine whether W is a subspace of V. (c.) Now, let V be a vector space over C and let u = |1 i and v = be vectors in V. Determine whether {u, v} is a basis for V. [1 0]
(2.) Let V be the vector space of M1x2(C) over R. (a.) Give a basis for V. (b.) Let W = { { 1] z €R. By using the definition of subspace, deter- mine whether W is a subspace of V. (c.) Now, let V be a vector space over C and let u = |1 i and v = be vectors in V. Determine whether {u, v} is a basis for V. [1 0]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
Related questions
Question
![(1.) Let a and b be vectors in R².
(a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain which
property is used in every step of derivation.
(b.) Let a = (a1, a2) and b= (b1, b2). The area(a, b) is given by a1b2 – azbı.
Compute the area in (a.) when a = (3, –2) and b= (1, 1).
(2.) Let V be the vector space of M1×2(C) over R.
(a.) Give a basis for V.
={{r 1] - €R.
(b.)
Let W
By using the definition of subspace, deter-
mine whether W is a subspace of V.
(c.) Now, let V be a vector space over C and let u =
be vectors in V. Determine whether {u, v} is a basis for V.
1 i and v =
[1 0]
(3.) Let V be the vector space of C² over R and W be the vector space of P1(C)
over R. Let T :V → W be a mapping defined by
T(x, y) = xi + (y – x)t.
%3D
(a.) Show that T is a linear transformation.
(b.) Determine whether T is an isomorphism.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60abd4de-ba2d-4a53-b8fc-e1d2e0799cec%2F9b97aba1-8cac-40e5-a956-ea76f2a99c6e%2Fkgi4wwr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1.) Let a and b be vectors in R².
(a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain which
property is used in every step of derivation.
(b.) Let a = (a1, a2) and b= (b1, b2). The area(a, b) is given by a1b2 – azbı.
Compute the area in (a.) when a = (3, –2) and b= (1, 1).
(2.) Let V be the vector space of M1×2(C) over R.
(a.) Give a basis for V.
={{r 1] - €R.
(b.)
Let W
By using the definition of subspace, deter-
mine whether W is a subspace of V.
(c.) Now, let V be a vector space over C and let u =
be vectors in V. Determine whether {u, v} is a basis for V.
1 i and v =
[1 0]
(3.) Let V be the vector space of C² over R and W be the vector space of P1(C)
over R. Let T :V → W be a mapping defined by
T(x, y) = xi + (y – x)t.
%3D
(a.) Show that T is a linear transformation.
(b.) Determine whether T is an isomorphism.
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