Linear Algebra

Let T : Rn-->Rn be a linear transformation, whose standard matrix is invertible. Show that if B = {v1, . . . , vn} is a basis for
Rn, then {T(v1), . . . ,T(vn)} is also a basis for Rn.

  1. 👍 0
  2. 👎 0
  3. 👁 96
asked by Alex

Respond to this Question

First Name

Your Response

Similar Questions

  1. Linear Algebra

    2. Suppose that T is a linear transformation from R2 to R4 such that T ((1, 1)) = (3, −1, 4, −3) and T ((2, −1)) = (3, −2, −1, −3). Determine the matrix of T (with respect to the standard bases). 3. Suppose that T is a

    asked by Ryan on October 18, 2015
  2. Math

    Determine whether or not the given linear transformation is invertible. If it is invertible, compute its inverse. (If the transformation is not invertible, enter IMPOSSIBLE. Use theta for θ.) Tθ:R2→R2, the reflection of the

    asked by Peter on March 10, 2016
  3. Linear Algebra

    Consider the linear transformation T: R^3->R^3 which acts by rotation around the y-axis by an angle of pi, followed by a shear in the x-direction by a factor of 2. a) Find the matrix for T. Explain your method. b) What is T(1,2,3)

    asked by Brody on March 5, 2014
  4. math

    If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column

    asked by mathstudent on January 8, 2007

    How to prove or disprove (a)if A has a zeronentryonthe diagonal then A is not invertible (b)if Ais not invertible then for every matrix B, AB is not invertible (c)if A is a nonzero 2X2 matrix such that A^2+A=0, then A is

    asked by LEON on October 24, 2010
  6. math

    Let f be the invertible linear transformation represented by the matrix A = (-2 -3 2 -3) Find in terms of x and y the equation of the image f(C) and of the unit circle C

    asked by s17 on February 5, 2017
  7. Algebra

    Let A and B be n x n matrices, assume AB is invertible and show that both A and B are invertible. what? AB is invertible -----> There exists a matrix X such that: (AB)X = 1 But (AB)X = A(BX). So, AY = 1 for Y = BX Also: X(AB) = 1

    asked by Ashley on May 31, 2007
  8. Math: Linear Algebra

    Let T1: P1 -> P2 be the linear transformation defined by: T1(c0 + c1*x) = 2c0 - 3c1*x Using the standard bases, B = {1, x} and B' = {1, x, x^2}, what is the transformation matrix [T1]B',B T(c0 + c1*x) = 2c0 - 3c1*x ---> T(1) = 2

    asked by mathstudent on June 9, 2007
  9. Math

    Let T: R^3 -> R^3 be a linear transformation whose matrix, with respect to the standard basis is |1 1 2| |1 3 0| |1 0 1|. If T^(-1){ |96| |u| | 2| = |v| | 3| |w|} then the value of v is?

    asked by Anonymous on August 24, 2012
  10. Diagonalize

    construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible. Just write down a diagonal matrix with one zero on the diagonal and then apply an orthogonal transformation. E.g. if you start with the matrix: A = [1

    asked by Jeff on July 12, 2007

More Similar Questions