Linear Algebra
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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
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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 
Linear Algebra
Consider the linear transformation T: R^3>R^3 which acts by rotation around the yaxis by an angle of pi, followed by a shear in the xdirection 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 
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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 
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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 
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 
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 
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
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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 
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