Homework for §3.4
Let




1 2 1
3
0 2
A =  9 3 6  and B =  1 −1 3  .
2 1 4
−2 1 9
1. Calculate 3A + B.
2. Calculate 4A − 2B.
.........................................................................................
Find the following matrix products
−1 6
2 3
3.
9 4
0 1


−1 9 2
0
3
4.  0 2 
1 0 2
−1 3



2
3 1
9 −1 4
5.  −1 −1 2   −3 2 0 
3
0 2
1
3 1
.........................................................................................
6. Let
A=
a b
c d
.
Find a 2 × 2 matrix L such that
LA =
a
b
c + ka d + kb
.
This shows that the elementary row operations can be thought of as a sequence of left multiplications by certain matrices. Proceed as follows:
ka kb
. (Multiply the 1st row by k)
(a) Find L1 such that L1 A is
c d
ka
kb
. (Add the 1st row to the 2nd row)
(b) Find L2 such that L2 (L1 A)) is
c + ka d + kb
a
b
(c) Find L3 such that L3 (L2 (L1 A)) is
. (Divide the first row by k)
c + ka d + kb
Then L = L3 L2 L1 .