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Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B...
Problem 4 Let T:R2 R2 be defined by and a be the standard basis for R2....
Problem 4 Let T:R2 R2 be defined by and a be the standard basis for R2. a) Find the matrix of T with respect to a, (T): b) Let 3 be the basis { 1 -1}. Find (T18 c) Find (7)
10. (10 pt) Let bi1 The set B tbi,b2) is a basis for R2. Let T...
10. (10 pt) Let bi1 The set B tbi,b2) is a basis for R2. Let T : R2 →R2 is a linear transformation such that T(bi) 7bi +7b2 and T (b2) 3bi +4b2 Then the matrix of T relative to the basis B is and b2- -1 4 [T]B and the matrix of T,relative to the standard basis E for R2 is
-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given...
-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given that L 2- 3 (a) Find the matrix A that represents L with respect to the basisu-| | 2-1 1-1 4 1 and the 6 standard basis F1 (b) Find the matrix B that represents IL with respect to the standard basis in both R3 and R2
Question 6 (2 pts). [Exercise 4.1.9] Let V = W = R 2 . Choose the...
Question 6 (2 pts). [Exercise 4.1.9] Let V = W = R 2 . Choose
the basis B = {x1, x2} of V , where x1 = (2, 3), x2 = (4, −5) and
choose the basis D = {y1, y2} of W, where y1 = (1, 1), y2 = (−3,
4). Find the matrix of the identity linear mapping I : V → W with
respect to these bases.
QUESTION 6 (2 pts). Exercise 4.1.9 Let V = W...
Problem 6. (6 points) (a) Explain why В-Q.(.)}form a basis for R2 forms a basis for...
Problem 6. (6 points) (a) Explain why В-Q.(.)}form a basis for R2 forms a basis for R2 (b) Find the coordinate vector of in the basis (c) Suppose the standard matrix of a linear transformation T:R2 R2 is 2-3 Find the matrix of T with respect to the basis B, i.e., find [T]B.
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That...
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
Exercise 2 Let B= (Po, P1, P2) be the standard basis for P2 and B= (91,92,93)...
Exercise 2 Let B= (Po, P1, P2) be the standard basis for P2 and B= (91,92,93) where: 91 = 1+2,92 = x+r2 and 43 = 2 + x + x2 1. Show that S is a basis for P2. 2. Find the transition matrix PsB 3. Find the transition matrix PB-5 4. Let u=3+ 2.c + 2.ra. Deduce the coordinate vector for u relative to S.
vectors pure and applied. exercise 6.4.2 OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with resp...
vectors pure and applied. exercise 6.4.2
OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with respect to some basis. Then β would have Proof Suppose t matrix representation D=(d, 0 say, with respect to that basis and ß2 would have matrix representation 2 (d2 0 with respect to that basis. However for all xj, so β-0 and β2...
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representat...
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a geometrical interpretation of T.
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a...
Problem 4 Let T:R2 R2 be defined by and a be the standard basis for R2. a) Find the matrix of T with respect to a, (T): b) Let 3 be the basis { 1 -1}. Find (T18 c) Find (7)
10. (10 pt) Let bi1 The set B tbi,b2) is a basis for R2. Let T : R2 →R2 is a linear transformation such that T(bi) 7bi +7b2 and T (b2) 3bi +4b2 Then the matrix of T relative to the basis B is and b2- -1 4 [T]B and the matrix of T,relative to the standard basis E for R2 is
-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given that L 2- 3 (a) Find the matrix A that represents L with respect to the basisu-| | 2-1 1-1 4 1 and the 6 standard basis F1 (b) Find the matrix B that represents IL with respect to the standard basis in both R3 and R2
Question 6 (2 pts). [Exercise 4.1.9] Let V = W = R 2 . Choose
the basis B = {x1, x2} of V , where x1 = (2, 3), x2 = (4, −5) and
choose the basis D = {y1, y2} of W, where y1 = (1, 1), y2 = (−3,
4). Find the matrix of the identity linear mapping I : V → W with
respect to these bases.
QUESTION 6 (2 pts). Exercise 4.1.9 Let V = W...
Problem 6. (6 points) (a) Explain why В-Q.(.)}form a basis for R2 forms a basis for R2 (b) Find the coordinate vector of in the basis (c) Suppose the standard matrix of a linear transformation T:R2 R2 is 2-3 Find the matrix of T with respect to the basis B, i.e., find [T]B.
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
Exercise 2 Let B= (Po, P1, P2) be the standard basis for P2 and B= (91,92,93) where: 91 = 1+2,92 = x+r2 and 43 = 2 + x + x2 1. Show that S is a basis for P2. 2. Find the transition matrix PsB 3. Find the transition matrix PB-5 4. Let u=3+ 2.c + 2.ra. Deduce the coordinate vector for u relative to S.
vectors pure and applied. exercise 6.4.2
OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with respect to some basis. Then β would have Proof Suppose t matrix representation D=(d, 0 say, with respect to that basis and ß2 would have matrix representation 2 (d2 0 with respect to that basis. However for all xj, so β-0 and β2...
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a geometrical interpretation of T.
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a...
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