This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 4. T (u) = 1. FALSE correct −7
10 5. T (u) = True or False? −9
11 6. T (u) = −7
11 2. TRUE
Explanation:
If A is m × n, then A has n columns, so
if A has m pivot columns, then m ≤ n. On
the other hand, TA : Rn → Rm is onetoone
if and only if the columns of A are linearly
independent. Explanation:
But the Fundamental Theorem, T is given
by the matrix mapping When m < n, however, the columns of A
are not linearly independent. For example,
the columns of the matrix
A= 1
0 01
11 Thus T : x → [T (e1 ) T (e2 ) T (e3 )] x x
2 −4 1 1 x2 .
=
−1 3 1
x3 are not linearly independent. FALSE . 009 T (u) = 10.0 points and T (e3 ) = 2
, T (e 2 ) =
−1 −4
,
3 1
, determine T (u) when
1 1
3 .
u=
2 −4
3 Consequently, If T : R3 → R2 is a linear transformation
such that
T (e 1 ) = 2
−1 T (u) = Consequently, the statement is 4 010 −8
10 1
1
3.
1
2 . 10.0 points If T : R3 → R2 is the linear transformation
such that x1
1
−4
2
+ x3
+ x2
T x2 = x1
1
1
3
x3
determine T (u) when 1
2.
u=
3 1. T (u) = −9
10 2. T (u) = −8
11 1. T (u) = −3
9 3. T (u) = −8
correct
10 2. T (u) = −2
8 khan (sak2454) – HW05 – gilbert – (57245)
3. T (u) = −4
9 4. T (u) = −4
8 5. T (u) = −3
correct
8 6. T (u) = −2
9 Explanation:
By deﬁnition, and T (e3 ) = −4
,
1 2
, T (e 2 ) =
3 T (e 1 ) = 1
.
1 Thus by the Fundamental Theorem, T is
given as a matrix mapping and so T : x → [T (e1) T (e2 ) T (e3 )] x x
2 −4 1 1 x2 ,
=
311
x3 T (u) = 2 −4
31 Consequently,
T (u) = 1
1
2.
1
3
−3
8 . 5...
View
Full
Document
This document was uploaded on 02/26/2014.
 Fall '14

Click to edit the document details