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7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so...
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...
that is Give an example of a linear transformation T: R2X2 → Ral surjective (onto), however...
that is Give an example of a linear transformation T: R2X2 → Ral surjective (onto), however is not one-to-one. O No linear transformation, T, exists which satisfies these conditions. There exist such a linear transformation, T. For example: sat
Find a linear transformation T : R 3 → M22 such that T 1...
Find a linear transformation T : R 3 → M22 such that T 1 2 4 = (
4 1 7 2 ) , T 0 3 5 = ( 0 7 2 4 ) , and T 2 0 2 = (
1 4 1 3 ) .
9. (4 marks) Find a linear transformation T:R3 M22 such that T | 2 = 1 ( 7 2...
Let T: P1 → P2 be a linear transformation defined by T(a + bx) = 3a...
Let T: P1 → P2 be a linear transformation defined by T(a + bx) = 3a – 2bx + (a + b)x². (a) Find range(T) and give a basis for range(T). (b) Find ker(T) and give a basis for ker(T). (c) By justifying your answer determine whether T is onto. (d) By justifying your answer determine whether T is one-to-one. (e) Find [T(7 + x)]], where B = {-1, -2x, 4x2}.
Let T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T) and give a basis...
Let T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T) and give a basis for range(T). (b) Find ker(T) and give a basis for ker(T) (c) By justifying your answer determine whether T is onto. (d) By justifying your answer determine whether T is one-to-one. (e) Find [T(7+x)]B, where B={−1,−2x,4x2} Please solve it in very detail, and make sure it is correct.
Let T:P1→P2T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2.T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T)range(T) and give a basis...
Let T:P1→P2T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2.T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T)range(T) and give a basis for range(T)range(T). (b) Find ker(T)ker(T) and give a basis for ker(T)ker(T). (c) By justifying your answer determine whether TT is onto. (d) By justifying your answer determine whether TT is one-to-one. (e) Find [T(7+x)]B[T(7+x)]B, where B={−1,−2x,4x2}B={−1,−2x,4x2}.
2) Let T be a linear transformation from P3(R) to M22(R). Let B= (1+2x + 4x2...
2) Let T be a linear transformation from P3(R) to M22(R). Let B= (1+2x + 4x2 + 8x3), (1 + 3x + 5x2 + 10x3), (1 + 4x + 7x2 + 13r%),(1 + 4x + 7x2 + 14x²). Let C= [] [ 1];[1 ] [ ] 0 17 40 Let M= 13 31 36 124 22 52 -61 -209 23 55 -64 -220 be the matrix transformation of T from basis B to C. -47 -161 The closed form of...
13. A linear transformation T takes Nº into f". T[ +y - y 2.1 + 3y...
13. A linear transformation T takes Nº into f". T[ +y - y 2.1 + 3y y (a) Is T one to one? Justify your answer. If not, then give two vectors with the same image. (b) Is T onto? Justify your answer. If not then give a vector in R? that is not an image.
If possible, write down an example of a matrix with the following properties. If it is...
If possible, write down an example of a matrix with the
following properties. If it is not possible to do so, write not
possible. You do not need to justify your reasoning.
A matrix AER2x2 such that T (7) = A7, where T is a linear transformation that reflects vectors in R2 about the line x1 = x2 and then projects them onto the 22 axis.
Question 8 [10 points] Suppose T: RM22 is a linear transformation whose action on a basis for R4 ...
Question 8 [10 points] Suppose T: RM22 is a linear transformation whose action on a basis for R4 is as follows -1 1 -11 4 4 0 1 1 0 1 -1 1 -45 1 2-2 1 -1 7 0 Determine whether T is one-to-one andlor onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is yt onto, show this by providing a matrix in M22 that is...
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...
that is Give an example of a linear transformation T: R2X2 → Ral surjective (onto), however is not one-to-one. O No linear transformation, T, exists which satisfies these conditions. There exist such a linear transformation, T. For example: sat
Find a linear transformation T : R 3 → M22 such that T 1 2 4 = (
4 1 7 2 ) , T 0 3 5 = ( 0 7 2 4 ) , and T 2 0 2 = (
1 4 1 3 ) .
9. (4 marks) Find a linear transformation T:R3 M22 such that T | 2 = 1 ( 7 2...
Let T: P1 → P2 be a linear transformation defined by T(a + bx) = 3a – 2bx + (a + b)x². (a) Find range(T) and give a basis for range(T). (b) Find ker(T) and give a basis for ker(T). (c) By justifying your answer determine whether T is onto. (d) By justifying your answer determine whether T is one-to-one. (e) Find [T(7 + x)]], where B = {-1, -2x, 4x2}.
2) Let T be a linear transformation from P3(R) to M22(R). Let B= (1+2x + 4x2 + 8x3), (1 + 3x + 5x2 + 10x3), (1 + 4x + 7x2 + 13r%),(1 + 4x + 7x2 + 14x²). Let C= [] [ 1];[1 ] [ ] 0 17 40 Let M= 13 31 36 124 22 52 -61 -209 23 55 -64 -220 be the matrix transformation of T from basis B to C. -47 -161 The closed form of...
13. A linear transformation T takes Nº into f". T[ +y - y 2.1 + 3y y (a) Is T one to one? Justify your answer. If not, then give two vectors with the same image. (b) Is T onto? Justify your answer. If not then give a vector in R? that is not an image.
If possible, write down an example of a matrix with the
following properties. If it is not possible to do so, write not
possible. You do not need to justify your reasoning.
A matrix AER2x2 such that T (7) = A7, where T is a linear transformation that reflects vectors in R2 about the line x1 = x2 and then projects them onto the 22 axis.
Question 8 [10 points] Suppose T: RM22 is a linear transformation whose action on a basis for R4 is as follows -1 1 -11 4 4 0 1 1 0 1 -1 1 -45 1 2-2 1 -1 7 0 Determine whether T is one-to-one andlor onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is yt onto, show this by providing a matrix in M22 that is...
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