Question

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 of R2 such that [T]g is diagonal for any T: R2R2 (b) If T is the reflection about a line l through the origin in R2, then there erists (1) Find T]e is just the E-matriz of T. so A= false, and justify your answers basis B for R2 such that Ts is

Answer 1

SOLUTION

T barin foriR2 () B any B {(a1,6),(4,b} Now chavje af basin matrix [Q t Now [T) B Q A Q b-a QT (2) bt A Then (G) . ) Aa 19 -61 i9o1b9 ban +4br Aait Ab

paib2tb b2 - n9i92-A92b) m fimt paib2tqb,b1-rai92-926 hm baibi- bi tpai4A9ib 3. (o) False TCy ) Consider Tl) () = "L_} tQ he qnn Cha of Co ordie t ma ri x San b b b hr - b a O O br bi b2 thi diajenal o obuato