(a) Find the matrix of T(x₁, x2) = (3x₁,4x1 x2, 0) with respect tothe standard bases.(b) Find the matrix of the linear map T : R² → R² given by rotationby 90° counterclockwise with respect to the standard bases.

(a) Find the matrix of T(x1, x2) the standard bases. = (3x₁, 4x₁ — x2, 0) with respect to - (b) Find the matrix of the linear map T : R² → R²2 given by rotation by 90° counterclockwise with respect to the standard bases.

(a) Find the matrix of T(x1, x2) the standard bases. = (3x₁, 4x₁ — x2, 0) with respect to - (b) Find the matrix of the linear map T : R² → R²2 given by rotation by 90° counterclockwise with respect to the standard bases.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Find a basis of the subspace of R* defined by the equation 5x1 - 7x2+8x3 6х4 = 0. 9. 9. 9. Basis: 9.…

Q: (a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor- mations L₁ and L2,…

A: (a)Two Linear transformations are mentioned:.Thus the matrix for the transformation is given by and…

Q: Let L: R → R be defined by L(au + Bu2) = (a+B)u1 + (a - B)u2, where u = (1, -1)', u2 = (2, 1)", and…

Q: Find the matrix A of the rotation about the z-axis through an angle of pi/2, counterclockwise as…

A: To get the matrix A for a rotation about the z-axis through an angle of pi/2 counterclockwise, we…

Q: L(p(x)) = - 6p' – 3p" maps P4 into P3. (a) Find the matrix representation of L with respect to the…

A: Given L:P4→P3 defined by Lpx=6p'−3p''. a We have to find the matrix representation of L with…

Q: L(p(x)) = 8p' + 4p" maps P4 into P3. (a) Find the matrix representation of L with respect to the…

Q: Show that any isometry of R^n which fixes the origin is linear, and hence must be of the form f(x) =…

A: Introduction A square matrix is said to be an orthogonal matrix if…

Q: (b) Consider the linear operator s 2: V V where s 2(v) is the vector v reflected in the line y =…

Q: Orthogonalize the basis {(1, 1, 1, 1),(1, 1, −1, −1),(0, −1, 2, 1)} by the Gram-Schimidt process.…

A: Let x1 = 1111 ; x2 = 11-1-1 ; x3 = 0-121 Using Gram schmidt process , we get orthogonal…

Q: Define a linear operator (transformation) on R2 by performing the following operations in order: (i)…

Q: Find an orthonormal basis of the plane ¤1 + 5x2 – x3 = 0. %3D

Q: 10. Let *-{0] [8] []} B B is a basis of R³. Let T: R³ R³ be the linear transformation given by T(v)…

Q: Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x,…

Q: Let X ∈ R3 be some xed vector with coordinates X1, X2, X3. Consider the action on vectors of the…

A: From the given information we get:

Q: (b) Prove that the following matrices are symplectic : (i) (ii) [1] matrix. where I is the nxn…

Q: d. Find the transition matrix from C to B. e. Find the coordinates of u = (2, –2) in the ordered…

Q: Determine the matrix that can be used to define a rotation through pi about the point (2, -1). Find…

A: To determine the matrix that can be used to define a rotation through π about the point (2, -1).

Q: For this actvity, find the matrix representation [7] for the linear transformation 7 : R³ → R²…

Q: Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix…

A: As per guidelines of bartleby we solve only first three parts.

Q: [2x1 – 3x2] - () = | ×1– 4x2 Let T X2 a) Show that T is a linear transformation map. b) Find a…

A: Solution:-

Q: Define the linear transformation T : P2 → P2 according to T (p(x)) = p(2x − 5). (a) Compute the…

A: Given T(p(x)) = p(2x − 5)

Q: The linear tranformation L defined by L(p(x)) = -13p' – 14p" maps P, into P3. (a) Find the matrix…

Q: How can I find [L] from basis B to basis C, if basis B = {1 + x + x^2, 1 + x, 2x + x^2} and basis C…

Q: Find the standard matrix representation for each linear operator L : R^2 → R^2 described below: (a)…

A: Solution is uploaded in next step

Q: The linear tranformation L defined by L(p(x)) = -2p' +9p" maps P4 into P3. (a) Find the matrix…

Q: Let L be the line that passes through the origin in the direction of u = (1, 1, 1). Find the matrix…

A: Let L be the line that passes through the origin in the direction of u = (1, 1, 1) The matrix for…

Q: Compute the standard matrix for the linear map T : R² → R² which (1) rotates i by 0 = T, (2)…

Q: The matrices 0 4₁ = [10], 4₂ = [8] · A3 rm a basis for the linear space V = R2x2. Write the matrix…

A: The matrix representation of a linear transformation is obtained by expressing the transformation of…

Q: Define a linear operator (transformation) on R2R2 by performing the following operations in order:…

Q: Let a and B be the standard bases for R" and R" respectively. For each of the following linear…

A: By bartleby rules, only first three sub parts have been answered Given linear transformation is…

Q: Let 0<θ<2π, θ ≠ π. Consider the linear transformation T: C^2→C^2 given by matrix [ cosθ -sinθ]…

Q: Find the standard matrix of the linear operator M : R R' that first project every vector through…

A: We have to find Standard Matrix of Linear Operator M : R3 -> R3

Q: Let = A = - = The cross product of two vectors in R³ is defined by a1 a2 az X b₁ b₂ b3 = 0 E] 7 Find…

Q: Draw the projection of b onto a and also compute it from p = îa: -=[] a = (a) b = cose 3] sin and…

Question

(a) Find the matrix of T(x₁, x2) = (3x₁,4x1 x2, 0) with respect to
the standard bases.
(b) Find the matrix of the linear map T : R² → R² given by rotation
by 90° counterclockwise with respect to the standard bases.

Expert Solution

Step 1

see below the answer and calculation

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

(a) From the vector space of polynomials of degree at most 3 to itself the following linear transformation is defined: T(f(x)) = (3x - 2)f'(x) Write the matrix of T for the standard basis. (b) A vertical shear of strength 2 is followed by rotation by 45 degrees applied to a vector v yielding the vector (4,4). What was the original vector v?
Find the matrix representation of the linear operator T relative to B1. Then use Theorem 15 to find [T]B2
Find a basis of the subspace of IR defined by the equation 871 - 7x2 - 4z3 = 0. Basis:
Find an orthonormal basis of the plane x₁ + x₂ + x3 = 0
Using linear algebra, show that G={p1(x)=1−x+x^2, p2(x)=x, p3(x)=x+x^2} is a basis of P2, the vector space of polynomials of degree at most two with real coefficients.
The matrices A₁ = A3 [] = ^--^- A₂ = [] =[] A4 form a basis for the linear space V = R 2x2. Write the matrix of the linear transformation T: R 2x2R 2x2 such that T(A) = 3A + 10AT relative to this basis.
Let S be the parallelogram then determine the area of parallelogram by the vectors [h | 1 and let A = h and [0 h+1] h=102 Also compute the area of the image of parallelogram under the linear transformation ""
Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.
Find an orthogonal diagonalization for A = [[1, 1,0], [1, 1, 1], [0, 1, 1]], i. e. find an orthogonal matrix U and a diagonal matrix D such that U^ (TT)AU = D. Any empty entries are assumed to be 0.