xn en x1 t e 1 x2 t e 2 xn t

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ty, T (x) = T (x1 e1 + x2 e2 + . . . + xn en ) = x1 T ( e 1 ) + x2 T ( e 2 ) + . . . + xn T ( e n ) . x1 x2 where A is the 2 × 2 matrix standard matrix [T (e1 ) T (e2 )] where T (ej ) is a vector in Rm . So for each x in Rn , T (x) is determined by its effect on e1 , e2 , . . . , en . Consequently, the statement is of T . Now 1 0 1 −2 True or False? Explanation: We can write R2 both as rows and column vectors x1 . (i) (x1 , x2 ) , (ii) x2 e1 = 2 A linear transformation T : Rn → Rm is completely determined by its effect on the columns e1 , e2 , . . . , en of the n × n identity matrix In . 2 01 2. A = 3 A= 1 2 −2 = T (e 2 ) . Consequently, Determine A so that T can be written as the matrix transformation TA : R2 → R2 . 1. A = 2 −2 TRUE . = (1, 0) , e2 = 0 1 = (0, 1) , so that T (1, 0) = (3, 1) = 3 1 008 10.0 points If A is an m × n matrix with m pivot columns, then the linear transformation = T (e 1 ) , TA : Rn → Rm , TA (x) = Ax khan (sak2454) – HW05 – gilbert – (57245) is one-to-one....
View Full Document

Ask a homework question - tutors are online