Anyone please solve this for me. Thank You!
Let T : R^m -> R^n be a linear transformation. For each of the following cases, list whether it is possible for T to be one-to-one, onto, both, or neither.
(a) m > n.
(b) m < n.
(c) m = n.
Homework Answers
The ans of above Question is m = n.
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T...
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Question 2. a) The zero transformation. We define the zero transformation, To: FN → Fm by...
Question 2. a) The zero transformation. We define the zero transformation, To: FN → Fm by To(x) = 0 VxEFN. (i) What is R(To)? (ii) Is To onto? (iii) What is N(To)? (iv) Is To one-to-one? (v) What is (To]s? b) The identity transformation. We define the identity transformation, Tj: Fn + En by Ty(x) = x V xEFN. (i) What is R(Ti)? (ii) Is T, onto? (iii) What is N(T)? (iv) Is T one-to-one? (v) What is Ti]s? Question...
Please can you explain the answers to this, particularly the first part. 14 (1.9.31, .35) Let...
Please can you explain the answers to this, particularly the first
part.
14 (1.9.31, .35) Let be a linear transformation and A its stan- dard matrix. (a) Complete the following statement to make it true: "T is one-to-one if and only if A has pivot columns." Explain why this statement is true. b) If T maps R" onto Rm", can you give a relation between m and n? (c) If T is one-to-one, what can you say about m and...
need help on this. thanks in advance Question 16 Determine whether the linear transformation T is...
need help on this. thanks in advance
Question 16 Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 1-23 -1 3-4 2 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R. One-to-one; not onto #3 One-to-one; onto a Not one-to-one; onto R3 Not one-to-one; not onto a
Determine whether the linear transformation is one-to-one, onto, or neither T: R^2 -> R^2 , T(x,y)...
Determine whether the linear transformation is one-to-one, onto, or neither T: R^2 -> R^2 , T(x,y) = (x-y,y-x)
7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so...
7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so that (a) T is one-to-one (b) T is not one-to-one but onto (c) T is neither one-to-one nor onto
Determine if there exists a linear transformation T: R2 -> R2 with the following properties. If...
Determine if there exists a linear transformation T: R2 -> R2
with the following properties.
If yes, give an example. If no, explain why such a
transformation is not possible.
(4) Determine if there exists a linear transformation T: R2 + R2 with the following properties. If yes, give an example. If no, explain why such a transformation is not possible. (a) T is one-to-one and onto. (b) T is not one-to-one. (c) T is not onto. (d) T is...
please answer both!! thank you 6. Is the transformation T: R → R defined T(x, y)...
please answer both!! thank you
6. Is the transformation T: R → R defined T(x, y) = (x + y, x - y + 1) a linear transformation? [3 marks] 8. Let A = 5 6 Find the eigenvalues and ONE of the corresponding 21 eigenvectors of A. [5 marks]
11.) Let T:R" - R"be a linear transformation. Prove T is onto if and only if...
11.) Let T:R" - R"be a linear transformation. Prove T is onto if and only if T is one-to-one. 12.) Let T:R" - R" and S:R" - R" be linear transformations such that TSX=X for all x ER". Find an example such that ST(x))+x for some xER". - .-.n that tidul,
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1,...
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Question 2. a) The zero transformation. We define the zero transformation, To: FN → Fm by To(x) = 0 VxEFN. (i) What is R(To)? (ii) Is To onto? (iii) What is N(To)? (iv) Is To one-to-one? (v) What is (To]s? b) The identity transformation. We define the identity transformation, Tj: Fn + En by Ty(x) = x V xEFN. (i) What is R(Ti)? (ii) Is T, onto? (iii) What is N(T)? (iv) Is T one-to-one? (v) What is Ti]s? Question...
Please can you explain the answers to this, particularly the first
part.
14 (1.9.31, .35) Let be a linear transformation and A its stan- dard matrix. (a) Complete the following statement to make it true: "T is one-to-one if and only if A has pivot columns." Explain why this statement is true. b) If T maps R" onto Rm", can you give a relation between m and n? (c) If T is one-to-one, what can you say about m and...
need help on this. thanks in advance
Question 16 Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 1-23 -1 3-4 2 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R. One-to-one; not onto #3 One-to-one; onto a Not one-to-one; onto R3 Not one-to-one; not onto a
7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so that (a) T is one-to-one (b) T is not one-to-one but onto (c) T is neither one-to-one nor onto
Determine if there exists a linear transformation T: R2 -> R2
with the following properties.
If yes, give an example. If no, explain why such a
transformation is not possible.
(4) Determine if there exists a linear transformation T: R2 + R2 with the following properties. If yes, give an example. If no, explain why such a transformation is not possible. (a) T is one-to-one and onto. (b) T is not one-to-one. (c) T is not onto. (d) T is...
please answer both!! thank you
6. Is the transformation T: R → R defined T(x, y) = (x + y, x - y + 1) a linear transformation? [3 marks] 8. Let A = 5 6 Find the eigenvalues and ONE of the corresponding 21 eigenvectors of A. [5 marks]
11.) Let T:R" - R"be a linear transformation. Prove T is onto if and only if T is one-to-one. 12.) Let T:R" - R" and S:R" - R" be linear transformations such that TSX=X for all x ER". Find an example such that ST(x))+x for some xER". - .-.n that tidul,
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...
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> Thank you so much!
Ahmed Jubaer Sat, Oct 2, 2021 8:27 AM