This preview shows page 1. Sign up to view the full content.
Unformatted text preview: he m × n matrix
A = [T (e1 ) T (e2 ) . . . T (en)]
with e1 , e2 , . . . , en the columns of the identity matrix In , then TA (x) = T (x). So T can
be identiﬁed with the matrix transformation
TA .
Consequently, the statement is
TRUE . then A x = x1 a 1 + x2 a 2 + · · · + xn a n
is a linear combination of the columns of A
with weights being the entries in x. Conversely, any linear combination
c1 a1 + c2 a2 + · · · + cn an
of the columns of A can be written as Ax with c1 c2 x = . .
.
.
cn Thus the range of TA consists of all linear
combinations of the columns of A.
Consequently, the statement is
TRUE . khan (sak2454) – HW05 – gilbert – (57245) 3 and
006 10.0 points Let T : R2 → R2 be the linear transformation such that
T (x1 , x2 ) = (3x1 + 2x2 , x1 − 2x2 ) . T (0, 1) = (2, −2) = 3 007 30 1 30 1 01 3. A = 2 3 4. A = 2 1 −2 . 10.0 points 1. FALSE
2. TRUE correct correct In row form Explanation:
For each x in Rn , x = In x = [ e 1 e 2 x1 x2 . . . en ] . .
. xn = x1 e 1 + x2 e 2 + . . . + xn e n . T (x1 , x2 ) = (3x1 + 2x2 , x1 − 2x2 ) ,
while in column vector form
T x1
x2 =A Thus by lineari...
View
Full
Document
This document was uploaded on 02/26/2014.
 Fall '14

Click to edit the document details