linear algebra
HhaNn
Math_21_HW_3__Intro_to_Linear_Transformations_and_Matrices.pdf
Linear Transformations, and their Standard Matrices
August 2, 2020
Question 1
a)Let A be the matrix A=
( 1 1 1 −3
) . Does there exist a vector ~x ∈ R2
such that A~x =
( 2 4
)
b)Let A be the matrix A=
1 1 −14 8 −12
0 6 −1
. Does there exist a vector ~x ∈ R3
such that A~x =
28
11
c) Let A be the matrix A=
1 1 00 1 −1
0 4 −4
. Does there exist a vector ~x ∈ R3
such that A~x =
1−1 −8
Question 2
Write the corresponding standard matrix for the following linear transfor- mations.
1
a) T
xy z
= (x− 2y
3z
)
b)T
xy z
=
x + 3zx−y
0
c)T
( x y
) =
2x−yx + y
3y
d)T
( x y
) =
x− 2yx + 6y
0
Question 3 Consider the following three matrices.
A =
1 0 00 2 0
0 3 4
B =
( 1 2 3 0 1 0
)
C =
1 21 1
0 3
Decide what products of these matrices exist, and compute all those that do. For example; BA exists but AB does not, so you would need to compute BA. (Hint; there will be 5 products that exist overall, don’t figure you can ”square” matrices sometimes)
2
