MATRICES AND INTEREST RATE.

Running Head: MATRICES AND INTEREST RATES
MATRICES AND INTEREST RATES
Name
Institute of Affiliation
Date

MATRICES AND INTEREST RATE 2
Question 1
i. ,
A=
[1 0
3 −5 ] , B=[−2 1
4 −3 ]
A +B = [ −2 1
4 −3 ] + [ 1 0
3 −5 ]
= [−1 1
7 −8 ]
ii. ,
2A - 3B =2 [ −2 1
4 −3 ] -3 [ 1 0
3 −5 ]
= [−4 2
8 −6 ] - [−3 0
−9 −15 ]
= [ −1 2
17 9 ]
iii. ,
AB= [−2 1
4 −3 ] . [1 0
3 −5 ]
= [ −2 1
−26 18 ]
iv. ,
AB+BA = [−2 1
4 −3 ] . [1 0
3 −5 ] +. [1 0
3 −5 ] .[−2 1
4 −3 ]
= [ −1 −4
−31 33 ]
b. ,
A= [ 3 2
−1 1 ]

MATRICES AND INTEREST RATE 3
B= [ 0 4
−2 8 ]
X=2A -B
= 2 [ 3 2
−1 1 ] - [ 0 4
−2 8 ]
= [ −2 1
−56 39 ]
c. ,
i.
A=[ 3 2
1 6 ]
Det A= (3 x 6) – (1 x 2)
=16
ii.
A−1 = 1
16 [ 6 −2
−1 3 ]
= [ 0.3750 −0.1250
−0.0625 0.1875 ]
iii. ,
AX=[ 5 6
7 2 ]
X= A−1
[ 5 6
7 2 ]
= [ 0.3750 −0.1250
−0.0625 0.1875 ]. [5 6
7 2 ]
= 1.5000 0.5000
2.5000 0.5000