Math 130 Worksheet 2: Linear algebra

... Math 130 Worksheet 2: Linear algebra ... but I thought this was a geometry class! ...

... Math 130 Worksheet 2: Linear algebra ... but I thought this was a geometry class! ...

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

... 3. Define rank and nullity of a vector space homomorphism T: U V. 4. Give a basis for the vector space F[x] of all polynomials of degree at most n. 5. If V is an inner product space, show that u, v w u, v u, w . 6. Define regular and singular linear transformation. 7. Give an example ...

... 3. Define rank and nullity of a vector space homomorphism T: U V. 4. Give a basis for the vector space F[x] of all polynomials of degree at most n. 5. If V is an inner product space, show that u, v w u, v u, w . 6. Define regular and singular linear transformation. 7. Give an example ...

1.2. Vector Space of n-Tuples of Real Numbers

... Note that some operators on either sides of these equations do not have the same meanings. For example, the + on the left of 2 denotes additions of real numbers while the + on the right denotes vector addition. Proof of the theorem is left as an exercise. ...

... Note that some operators on either sides of these equations do not have the same meanings. For example, the + on the left of 2 denotes additions of real numbers while the + on the right denotes vector addition. Proof of the theorem is left as an exercise. ...

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

... 20.) a.) If U and V are vector spaces over F, and if T is a homomorphism of U onto V with kernel W, then prove that CB ≃ . b.) If V is a finite - dimensional inner product space and if W is a subspace of V, then prove that = ⊕ F . 21.) Prove that every finite - dimensional inner product space has an ...

... 20.) a.) If U and V are vector spaces over F, and if T is a homomorphism of U onto V with kernel W, then prove that CB ≃ . b.) If V is a finite - dimensional inner product space and if W is a subspace of V, then prove that = ⊕ F . 21.) Prove that every finite - dimensional inner product space has an ...

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... Let X be a set. Let U be a family of subsets of X × X such that U is a filter, and that every element of U contains the diagonal relation ∆ (reflexive). Consider the following possible “axioms”: 1. for every U ∈ U, U −1 ∈ U 2. for every U ∈ U, there is V ∈ U such that V ◦ V ∈ U , where U −1 is defin ...

... Let X be a set. Let U be a family of subsets of X × X such that U is a filter, and that every element of U contains the diagonal relation ∆ (reflexive). Consider the following possible “axioms”: 1. for every U ∈ U, U −1 ∈ U 2. for every U ∈ U, there is V ∈ U such that V ◦ V ∈ U , where U −1 is defin ...