Question 5. (20 pts) Let T : R2 + R'be a linear transformation such that T(21,22)...
Question 5. (20 pts) Let T: R² + R* be a linear transformation such that T(21, 12) = (x1 - 2x2, -21 +3.22, 3.21 - 202). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
: Question 5. (20 pts) Let T : R² + R be a linear transformation such that T(21,02) = (1 - 2.62,-01 +3.62, 3.01 - 2.2). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
Find the standard matrix of T ( Call it A) Is T one-to-one? Justify your answer Is T onto ? Justify your answer -> Question 5. (20 pts) Let T : R? R? be a linear transformation such that T(:21,22) = (21 - 222, -21 +3.22, 3.11 - 2:02). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
R2 defined as Consider the linear transformation T: R2 T(21,22)=(0,21 – 22) Find the standard matrix for T: a ab sin (a) f 8 ат What is the dimensi of ker(T)? Is T one-to-one? Enter one: yes no Write the standard matrix for HoT, where H is the reflection of R2 about the 3-axis. a sin(a) f 22 8 R a E är (Alt + A)
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
X1 Let x = V = and v2 - and let T: R2R2 be a linear transformation that maps x into xxv, + XxV2. Find a matrix A such that T(x) is Ax for each x. X2 A= Assume that is a linear transformation. Find the standard matrix of T. T:R3-R2, T(41) = (1,3), and T(62) =(-4,6), and T(03) = (3. – 2), where e1, 22, and ez are the columns of the 3*3 identity matrix. A= (Type an integer...
QUESTION 1. §1.9 THE MATRIX OF A LINEAR TRANSFORMATION Le t T R be the linear transformation defined by t-th AnSwer Find the standard matrix of T. Is T one to one? Is T onto? Jushif'cahon
(1 point) Let f:R → R'be the linear transformation defined by T 4 -5 51 f(T) = -1 2 - 5 . | -4 0 3 Let B = {(-2,-1, 1), (-2, -2,1),(-1,-1,0)}, C = {{-2, -1, 1), (2,0, -1),(-1,1,0)}, be two different bases for R3. Find the matrix f for f relative to the basis B in the domain and C in the codomain. IT 3
Q8 6 Points Let T : R2 + Rº be a linear transformation with PT(x) = x2 – 1. Decide whether or not such a T is always diagonalizable. Justify your answer.. Q8.2 3 Points Determine/Compute the linear transformation T2 : R2 + R2, VH T(T(u)).