Linear Algebra MA233
1. Let T:R5!R3be a MAP THAT WE WOULD LIKE TO BE a linear transformation.
Let T(v1) = u1; T (v2) = u2; T (v3) = u3; T (v4) = u4; T (v5) = u5:
Let v1=
2
6
6
6
6
4
1
0
0
0
0
3
7
7
7
7
5
; v2=
2
6
6
6
6
4
1
1
0
0
0
3
7
7
7
7
5
; v3=
2
6
6
6
6
4
1
2
1
0
0
3
7
7
7
7
5
; v4=
2
6
6
6
6
4
2
3
1
4
2
3
7
7
7
7
5
; v5=
2
6
6
6
6
4
2
1
2
B
2
3
7
7
7
7
5
:
Let u1=2
4
1
1
2
3
5; u2=2
4
2
2
1
3
5; u3=2
4
2
3
2
3
5; u4=2
4
2
2
4
3
5u5=2
4
1
5
0
3
5
(a) Show that B can be 0.
(b) What value(s) can’t B be? Give a valid reason.
2. Let T:R5!R3be a linear transformation.
Let T(v1) = u1; T (v2) = u2; T (v3) = u3; T (v4) = u4; T (v5) = u5:
Let v1=
2
6
6
6
6
4
1
0
0
0
0
3
7
7
7
7
5
; v2=
2
6
6
6
6
4
1
1
0
0
0
3
7
7
7
7
5
; v3=
2
6
6
6
6
4
1
2
1
0
0
3
7
7
7
7
5
; v4=
2
6
6
6
6
4
2
3
1
4
2
3
7
7
7
7
5
; v5=
2
6
6
6
6
4
2
1
2
0
2
3
7
7
7
7
5
:
Let u1=2
4
1
1
2
3
5; u2=2
4
2
2
1
3
5; u3=2
4
2
3
2
3
5; u4=2
4
2
2
4
3
5u5=2
4
1
5
0
3
5
(a) What is the matrix representation of T. You need to compute an inverse of a matrix.
1
