linear alg please answer all of 4, if you dont want to answer 2 4. Let...

Question

Question

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 b

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 -

(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 trans

linear alg please answer all of 4, if you dont want to answer 2

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x)...

Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x) = Ax, where 1 0 2 -1 1 5 1) Find a basis for the kernel of T. 2) Determine the dimension of the kernel of T 3) Find a basis for the image(range) of T. 4) Determine the dimension of the image(range) of T. 5) Determine if it is a surjection or injection or both. 2 6) Determine whether or not v |0|...
3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin,...

3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin, and let S : R2 + R2 be the shear along the y-axis given by S(x,y) = (x,x+y). (You may assume that these are linear transformations.) (a) Write down, or compute, the standard matrix representations of T and S. (b) Use (a) to find the standard matrix representations of (i) SoT (T followed by S), and (ii) ToS (S followed by T). (c) Let...
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...

please help me with questions 1，2，3 1. Let V be a 2-dimensional vector space with basis...

please help me with questions 1，2，3 1. Let V be a 2-dimensional vector space with basis X = {v1, v2}, write down the matrices [0]xx and [id]xx. 2. Let U, V, W be vector spaces and S:U +V, T:V + W be linear transforma- tions. Define the composition TOS:U + W by To S(u) = T(S(u)) for all u in U. a. Show that ToS is a linear transformation. b. Now suppose U is 1-dimensional with basis X {41}, V...
Question 1: (4+4 =8 Marks) [a] Show that the transformation 7(x, y) = (7x - 3y:...

Question 1: (4+4 =8 Marks) [a] Show that the transformation 7(x, y) = (7x - 3y: 5x - 2y) of R4 R4 is a linear and give the matrix representation "A" of T with respect to the standard basis B={(1,0),0,1)). Furthermore, prove that T is invertible and find the preimage of the vector (1,-4). [b] Consider the transformation T: P3 → Pz defined by Tax3 + bx? +cx+d) = (a +2d)x? +(6+20)x² +(a+c+d)x. Determine Ker(T) and Range(T); and find a...
linear algebra: show all work please ned by Xi = I Find a basis 4. Let...

linear algebra: show all work please ned by Xi = I Find a basis 4. Let S be the subspace of R4 spanned b (1,0, 2, 1)? and x2 = (0, 1, 3, -2)7. Find for St.

3. Let E be the standard basis for R4. You know the following about the linear...

3. Let E be the standard basis for R4. You know the following about the linear transformation T: R-+ IR4. r-y (a) (2 points) Find a matrix for T in the standard basise., find [Tle) 1-1 0 0 0 1-1 0 0 0 1 -1 1 0 0 1 our n detai puase 13 (b) (2 points) Give a basis for the null space of T. How do you qe this Answes A basis is (c)(2 points) Give a basis...
Ler L: R4 → R3 be the linear transformation defined by (4p) L(z,y,z, t) = (x...

Ler L: R4 → R3 be the linear transformation defined by (4p) L(z,y,z, t) = (x – y +t, 2x – 2, Y + 2z – t) a) Find the images of the standard basis of RA L(1,0,0,0) = L(0,1,0,0) = L(0,0,1,0) = L(0,0,0,1) = b) Find a basis and the dimension of the image of L c) Find a basis and the dimension of the kernel of L (8p) (8p)
Part 1. (Trigonometry - Complex Arithmetic - Linear Algebra) For any real number 0, let Re...

Part 1. (Trigonometry - Complex Arithmetic - Linear Algebra) For any real number 0, let Re R2R be the linear transformation that is written in the standard basis as cosθ -sin θ sin cos 1.1. Draw a picture of the image of the unit square via R/s Describe the transformation in common words. 1.2. Compute det Re 1.3. Find (Re)-1 as a matrix. 1.4. Draw the image of the unit square via (R/s) How does this correspond to your description...

25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by...

25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0,...