Download Suggested Problems, Matrix multiplication, Inverses of matrices

Suggested Problems, Matrix multiplication, Inverses of matrices , Math 307, Fall 2015
1. Find the product AB for
1 −1 1
2
4
a) A = 2
and B = 3
.
−1 1
−1 −2


−1 −2
1 1 −2 5


4 −2 and B =
b) A =
.
1 3 3 −4
2
2




−3 3
1 2 3
0
−3 2 
.
c) A = 1 2 1 −1 and B = 
3
1
2 1 −1 3
1 −1
 1 
3


0 
1 −1 32 1 1


1 
d) A = − 2 0 0 1 1  and B = 
.

−1 
1 −1
3
1
−1
3
2


2 3 −1
2 0 1 

e) A = 2 −2 2 1 and B = 
1 1 −1 .
2
2
0 0 0
√
x1
2
ln(2)
and B =
f) A =
.
1
2
x2
sin( 2 )
e
2. Find the inverse of A for
−1 1
a) A =
.
3 2


1 0 0
b) A = 0 2 1 .
1 0 −1


1 1 1
c) A = 2 1 1 .
0 1 −1


1 0 2 2
−2 1 0 −2

d) A = 
−1 0 0 1 .
−2 1 1 0
2 3
3. Find the inverse of A =
. Use this result to solve the system
1 1
2x + 3y = 12
.
x+y =2
1


1 2 −1
0 . Use this result to solve the system
4. Find the inverse of A = 0 3
1 −1 1

 x + 2y − z = 1
3y = −2
.

x−y+z =3
2