MTH212 Answers | Campusflava https://campusflava.com Tutors, Past Questions and Projects. Tue, 22 Feb 2022 11:40:32 +0000 en-US hourly 1 https://wordpress.org/?v=6.6.3 https://i0.wp.com/campusflava.com/wp-content/uploads/2023/01/cropped-CF.png?fit=32%2C32&ssl=1 MTH212 Answers | Campusflava https://campusflava.com 32 32 123014824 MTH212 Solutions https://campusflava.com/blog/mth212-solutions/ https://campusflava.com/blog/mth212-solutions/#respond Wed, 12 Jan 2022 09:44:19 +0000 https://campusflava.com/blog/mth212-solutions/ MTH212 Tma Solutions 1. Linear transformations are also called vector space __________________ Isomorphism Inverse —>> homomorphisms. Dimension 2. The rank of T is defined to be the _______________________of R(T), the range space of T. projection Kernel function —>> dimension 3. There are two sets which are associated with any linear transformation, T. These are the […]

The post MTH212 Solutions first appeared on Campusflava.]]> MTH212 Tma Solutions

1. Linear transformations are also called vector space __________________

Isomorphism

Inverse

—>> homomorphisms.

Dimension

2. The rank of T is defined to be the _______________________of R(T), the range space of T.

projection

Kernel

function

—>> dimension

3. There are two sets which are associated with any linear transformation, T. These are the range and the ___________________of T

Projection

—>> Kernel

Function

Inverse

4. If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________

—>> \(V and U\)

\(U and T^{-1}\)

\(V^{-1} and U\)

\(V and T^{-1}\)

5. Let T:U→V be a linear transformation; If T is injective, we also say T is ______________________

Onto

Surjective

one-zero

—>> one-one

6. The __________________operator is both one-one and onto

Inverse

—>> Identity

Dimension

Range

7. Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an

The post MTH212 Solutions first appeared on Campusflava.]]> https://campusflava.com/blog/mth212-solutions/feed/ 0 70683 Let U be a vector space over F. Then space L(U,F) is called the _______________of \(U^{*}\) https://campusflava.com/blog/let-u-be-a-vector-space-over-f-then-space-luf-is-called-the-_______________of-u/ https://campusflava.com/blog/let-u-be-a-vector-space-over-f-then-space-luf-is-called-the-_______________of-u/#respond Wed, 12 Jan 2022 09:42:39 +0000 https://campusflava.com/blog/let-u-be-a-vector-space-over-f-then-space-luf-is-called-the-_______________of-u/ Let U be a vector space over F. Then space L(U,F) is called the _______________of \(U^{*}\) dual function function space —>> dual space map space

The post Let U be a vector space over F. Then space L(U,F) is called the _______________of \(U^{*}\) first appeared on Campusflava.]]> Let U be a vector space over F. Then space L(U,F) is called the _______________of \(U^{*}\)

dual function

function space

—>> dual space

map space

The post Let U be a vector space over F. Then space L(U,F) is called the _______________of \(U^{*}\) first appeared on Campusflava.]]> https://campusflava.com/blog/let-u-be-a-vector-space-over-f-then-space-luf-is-called-the-_______________of-u/feed/ 0 70681 Two finite-dimensional vector spaces U and V are isomorphic if and only if ______________ https://campusflava.com/blog/two-finite-dimensional-vector-spaces-u-and-v-are-isomorphic-if-and-only-if-______________/ https://campusflava.com/blog/two-finite-dimensional-vector-spaces-u-and-v-are-isomorphic-if-and-only-if-______________/#respond Wed, 12 Jan 2022 09:42:31 +0000 https://campusflava.com/blog/two-finite-dimensional-vector-spaces-u-and-v-are-isomorphic-if-and-only-if-______________/ Two finite-dimensional vector spaces U and V are isomorphic if and only if ______________ \(\frac{dimU}{pm}\) dimV \(dimU> dimV\) \(dimU> >dimV\) —>> \(dimU= dimV\)

The post Two finite-dimensional vector spaces U and V are isomorphic if and only if ______________ first appeared on Campusflava.]]> Two finite-dimensional vector spaces U and V are isomorphic if and only if ______________

\(\frac{dimU}{pm}\) dimV

\(dimU> dimV\)

\(dimU> >dimV\)

—>> \(dimU= dimV\)

The post Two finite-dimensional vector spaces U and V are isomorphic if and only if ______________ first appeared on Campusflava.]]> https://campusflava.com/blog/two-finite-dimensional-vector-spaces-u-and-v-are-isomorphic-if-and-only-if-______________/feed/ 0 70680 Let \(T:U \rightarrow V\) be a linear transformation; T is called _______________ if, for \(u_1,u_2\epsilon U,\) with , we have \(T(u_1 ) \notin T(u_2 ) \) https://campusflava.com/blog/let-tu-rightarrow-v-be-a-linear-transformation-t-is-called-_______________-if-for-u_1u_2epsilon-u-with-we-have-tu_1-notin-tu_2/ https://campusflava.com/blog/let-tu-rightarrow-v-be-a-linear-transformation-t-is-called-_______________-if-for-u_1u_2epsilon-u-with-we-have-tu_1-notin-tu_2/#respond Wed, 12 Jan 2022 09:42:26 +0000 https://campusflava.com/blog/let-tu-rightarrow-v-be-a-linear-transformation-t-is-called-_______________-if-for-u_1u_2epsilon-u-with-we-have-tu_1-notin-tu_2/ Let \(T:U \rightarrow V\) be a linear transformation; T is called _______________ if, for \(u_1,u_2\epsilon U,\) with , we have \(T(u_1 ) \notin T(u_2 ) \) —>> one-one Surjective one-zero Onto

The post Let \(T:U \rightarrow V\) be a linear transformation; T is called _______________ if, for \(u_1,u_2\epsilon U,\) with , we have \(T(u_1 ) \notin T(u_2 ) \) first appeared on Campusflava.]]> Let \(T:U \rightarrow V\) be a linear transformation; T is called _______________ if, for \(u_1,u_2\epsilon U,\) with , we have \(T(u_1 ) \notin T(u_2 ) \)

—>> one-one

Surjective

one-zero

Onto

The post Let \(T:U \rightarrow V\) be a linear transformation; T is called _______________ if, for \(u_1,u_2\epsilon U,\) with , we have \(T(u_1 ) \notin T(u_2 ) \) first appeared on Campusflava.]]> https://campusflava.com/blog/let-tu-rightarrow-v-be-a-linear-transformation-t-is-called-_______________-if-for-u_1u_2epsilon-u-with-we-have-tu_1-notin-tu_2/feed/ 0 70679 Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an ———-between U and V https://campusflava.com/blog/let-u-and-v-be-vector-spaces-over-a-field-f-and-let-tu-rightarrow-v-be-a-one-one-and-onto-linear-transformation-the-t-is-called-an-between-u-and-v/ https://campusflava.com/blog/let-u-and-v-be-vector-spaces-over-a-field-f-and-let-tu-rightarrow-v-be-a-one-one-and-onto-linear-transformation-the-t-is-called-an-between-u-and-v/#respond Wed, 12 Jan 2022 09:42:21 +0000 https://campusflava.com/blog/let-u-and-v-be-vector-spaces-over-a-field-f-and-let-tu-rightarrow-v-be-a-one-one-and-onto-linear-transformation-the-t-is-called-an-between-u-and-v/ Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an

The post Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an ———-between U and V first appeared on Campusflava.]]> Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an

The post Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an ———-between U and V first appeared on Campusflava.]]> https://campusflava.com/blog/let-u-and-v-be-vector-spaces-over-a-field-f-and-let-tu-rightarrow-v-be-a-one-one-and-onto-linear-transformation-the-t-is-called-an-between-u-and-v/feed/ 0 70678 The __________________operator is both one-one and onto https://campusflava.com/blog/the-__________________operator-is-both-one-one-and-onto/ https://campusflava.com/blog/the-__________________operator-is-both-one-one-and-onto/#respond Wed, 12 Jan 2022 09:42:14 +0000 https://campusflava.com/blog/the-__________________operator-is-both-one-one-and-onto/ The __________________operator is both one-one and onto Inverse —>> Identity Dimension Range

The post The __________________operator is both one-one and onto first appeared on Campusflava.]]> The __________________operator is both one-one and onto

Inverse

—>> Identity

Dimension

Range

The post The __________________operator is both one-one and onto first appeared on Campusflava.]]> https://campusflava.com/blog/the-__________________operator-is-both-one-one-and-onto/feed/ 0 70677 Let T:U→V be a linear transformation; If T is injective, we also say T is _________ _____________ https://campusflava.com/blog/let-tua%e2%80%a0v-be-a-linear-transformation-if-t-is-injective-we-also-say-t-is-_________-_____________/ https://campusflava.com/blog/let-tua%e2%80%a0v-be-a-linear-transformation-if-t-is-injective-we-also-say-t-is-_________-_____________/#respond Wed, 12 Jan 2022 09:42:05 +0000 https://campusflava.com/blog/let-tua%e2%80%a0v-be-a-linear-transformation-if-t-is-injective-we-also-say-t-is-_________-_____________/ Let T:U→V be a linear transformation; If T is injective, we also say T is ______________________ Onto Surjective one-zero —>> one-one

The post Let T:U→V be a linear transformation; If T is injective, we also say T is _________ _____________ first appeared on Campusflava.]]> Let T:U→V be a linear transformation; If T is injective, we also say T is ______________________

Onto

Surjective

one-zero

—>> one-one

The post Let T:U→V be a linear transformation; If T is injective, we also say T is _________ _____________ first appeared on Campusflava.]]> https://campusflava.com/blog/let-tua%e2%80%a0v-be-a-linear-transformation-if-t-is-injective-we-also-say-t-is-_________-_____________/feed/ 0 70676 If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________ https://campusflava.com/blog/if-t-is-an-isomorphism-between-u-and-v-then-t-1-is-an-isomorphism-between________________________/ https://campusflava.com/blog/if-t-is-an-isomorphism-between-u-and-v-then-t-1-is-an-isomorphism-between________________________/#respond Wed, 12 Jan 2022 09:42:04 +0000 https://campusflava.com/blog/if-t-is-an-isomorphism-between-u-and-v-then-t-1-is-an-isomorphism-between________________________/ If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________ —>> \(V and U\) \(U and T^{-1}\) \(V^{-1} and U\) \(V and T^{-1}\)

The post If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________ first appeared on Campusflava.]]> If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________

—>> \(V and U\)

\(U and T^{-1}\)

\(V^{-1} and U\)

\(V and T^{-1}\)

The post If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________ first appeared on Campusflava.]]> https://campusflava.com/blog/if-t-is-an-isomorphism-between-u-and-v-then-t-1-is-an-isomorphism-between________________________/feed/ 0 70675 Linear transformations are also called vector space __________________ https://campusflava.com/blog/linear-transformations-are-also-called-vector-space-__________________/ https://campusflava.com/blog/linear-transformations-are-also-called-vector-space-__________________/#respond Wed, 12 Jan 2022 09:41:54 +0000 https://campusflava.com/blog/linear-transformations-are-also-called-vector-space-__________________/ Linear transformations are also called vector space __________________ Isomorphism Inverse —>> homomorphisms. Dimension

The post Linear transformations are also called vector space __________________ first appeared on Campusflava.]]> Linear transformations are also called vector space __________________

Isomorphism

Inverse

—>> homomorphisms.

Dimension

The post Linear transformations are also called vector space __________________ first appeared on Campusflava.]]> https://campusflava.com/blog/linear-transformations-are-also-called-vector-space-__________________/feed/ 0 70674 The rank of T is defined to be the _______________________of R(T), the range space of T. https://campusflava.com/blog/the-rank-of-t-is-defined-to-be-the-_______________________of-rt-the-range-space-of-t/ https://campusflava.com/blog/the-rank-of-t-is-defined-to-be-the-_______________________of-rt-the-range-space-of-t/#respond Wed, 12 Jan 2022 09:41:50 +0000 https://campusflava.com/blog/the-rank-of-t-is-defined-to-be-the-_______________________of-rt-the-range-space-of-t/ The rank of T is defined to be the _______________________of R(T), the range space of T. projection Kernel function —>> dimension

The post The rank of T is defined to be the _______________________of R(T), the range space of T. first appeared on Campusflava.]]> The rank of T is defined to be the _______________________of R(T), the range space of T.

projection

Kernel

function

—>> dimension

The post The rank of T is defined to be the _______________________of R(T), the range space of T. first appeared on Campusflava.]]> https://campusflava.com/blog/the-rank-of-t-is-defined-to-be-the-_______________________of-rt-the-range-space-of-t/feed/ 0 70673