# linear alg please answer all of 4, if you dont want to answer 2 4. Let...   4. Let T: R4 + R3 be the transformation T(7) = A7 where A is the following matrix: . 1 1 0 1 A=-2 4 2 2 -1 8 3 5 (a) Find a basis for the range of T and its dimension. (b) The preimage of 7 is the set of all 7 € R4 such that T(T) = 7. Explain how the preimage of o is related to the null space of A. (c) Find a basis for the preimage of 7 and its dimension.
2. Let T(T) = Af and S(T) = Bī be the transformations that correspond to the following matrices: A= C. 3 -1 0 1 2 2 1 3 2 1 -1 0 2 1 2
(b) Find the image T(T) of ī= 3 2 (e) Find the image S(y) where y is your answer to (b). (d) The composition SoT is the transformation defined by SoT(T) = S(T(7)). Find the image SoT(T) of t= ( 3 2 Similar Homework Help Questions
• ### M 26.5. Let T :V →W be a linear transformation: let Theore T c(w)-*(V) be the dual transformation... Verify (2) and (3) of Theorem 26.5. m 26.5. Let T :V →W be a linear transformation: let Theore T c(w)-*(V) be the dual transformation. Then: (1) T* is linear. (3) If S : W → X is a linear transformation, then (SoT)" f = T(S* f). Proof. The proofs are straightforward. One verifies (1), for instance, as follows: whence T. (af + bg) = a T* f + bT" g. ロ The following diagrams illustrate property (3): c*(W) S*...

• ### Please answer correctly. i will not rate if it’s not correct and includes steps. Thank you. ex..2 please answer correctly. i will not rate if it’s not correct and includes steps. Thank you. ex..2 3 4-6 -8 0 -1 31 Find a besis for the image of T and a basis for the kornel of T. (Thse bases sed not be orthonormal) 2. (10 points) Let V be the linear subspace of R consisting of all vectors that satisty z Here, z, denotes the ith componest of a vector E.) 3r2 and (a) What is the dimension...

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• ### Let T: R - RS be a linear transformation such that T(1,0,0) = (4, 2, -1),... Let T: R - RS be a linear transformation such that T(1,0,0) = (4, 2, -1), T(0, 1, 0) = (1, -2, 3), and T0, 0, 1) = (-2,2,0). Find the indicated image. T(1, 0, -3) T(1, 0, -3) =

• ### How was the linear transformation of b1 and b2 were applied (L(b1) , L(b2))? NOTE: b1=(1,1)^T , b2=(-1,1)^T Linear Transformations EXAMPLE 4 Let L be a linear transformation mapping R? into itself an... How was the linear transformation of b1 and b2 were applied (L(b1) , L(b2))? NOTE: b1=(1,1)^T , b2=(-1,1)^T Linear Transformations EXAMPLE 4 Let L be a linear transformation mapping R? into itself and defined by where (bi, b2] is the ordered basis defined in Example 3. Find the matrix A represent- ing L with respect to [bi, b2l Solution Thus, A0 2 onofosmation D defined by D(n n' maps P into P, Given the ordered Linear Transformations EXAMPLE 4 Let...

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• ### Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A us... Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...

• ### 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...

• ### Let and let T : R4 → R4 be the map T(v) = v-2 proju,V-2 proju, w (a) Show that T is a linear tran... Let and let T : R4 → R4 be the map T(v) = v-2 proju,V-2 proju, w (a) Show that T is a linear transformation. (b) Find T] and (c) Show that T is invertible and find T-1 Let and let T : R4 → R4 be the map T(v) = v-2 proju,V-2 proju, w (a) Show that T is a linear transformation. (b) Find T] and (c) Show that T is invertible and find T-1

• ### Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem... Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...

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