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100
MATRICES
Addition of Matrices
*
sdrc
qbpa
sr
qp
dc
ba
Subtraction of Matrices
*
sdrc
qbpa
sr
qp
dc
ba
Multiplication of a matrix by a number k
* k
kdkckbka
dcba
Multiplication of two matrices
1) bqapq
pba
2)
bqbp
aqapqp
b
a
3)
dqcp
bqap
q
p
dc
ba
4)
dscqdrcp
bsaqbrap
sr
qp
dc
ba
Inverse Matrix
If A =
dc
ba, then inverse of A,
A-1 =
ac
bd
bcad
1 adbc is known as determinant.
A-1
does not exist if the determinant is zero
I is Identity Matrix = [ ]
A I = A
A A-1 = I = A-1 A
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101
1 (a) Given the matrix equation
10
01
01
32
1
30
pk , find the value of k
and ofp.(b) Hence, by using matrices, solve the following
simultaneous linear equations:
32
23
yx
y
[6 marks]
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7/31/2019 11. N
3/12
102
2 Mis a 2 2 matrix such that M
42
53=
10
01
(a) Find the matrixM.(b) Write the following simultaneous linear
equations as matrix equation:
642
253
qp
qp
Hence, using matrices, calculate the value ofp and ofq.
[6 marks]
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7/31/2019 11. N
4/12
103
3 (a) The inverse of matrix
32
95is
5
931
qp.
Find the value ofp and ofq.(b) By using matrices, calculate the
value ofx and ofy that satisfy the following
simultaneous linear equations:
132
695
yx
yx
[6 marks]
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7/31/2019 11. N
5/12
104
4 Mis a 2 2 matrix such that M
12
53=
12
53
(a) Find the matrixM.(b) Write the following simultaneous linear
equations as matrix equation:
92
1753
yx
yx
Hence, using matrices, calculate the value ofx and ofy.
[6 marks]
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7/31/2019 11. N
6/12
105
5 It is given that matrixM=
23
21, matrixN=
13
21 q
pand
10
01MN .
(a) Find the value ofp and ofq.
(b) Hence using matrices, solve the following equation:
3
11
23
21
y
x
[6 marks]
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7/31/2019 11. N
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106
6 (a) Find the inverse matrix of
21
24.
(b) By using matrices, calculate the value ofx and ofy that
satisfy the followingsimultaneous linear equations:
92
1424
yx
yx
[6 marks]
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7/31/2019 11. N
8/12
107
7 (a) Given matrix
57
46A , find the inverse matrix ofA.
(b) By using matrices, calculate the value ofm and of n that
satisfy the followingsimultaneous linear equations:
957
846
nm
nm
[6 marks]
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7/31/2019 11. N
9/12
108
8 (a) The inverse of matrix
45
21is
15
4 rn .
Find the value of n and ofr.(b) By using matrices, calculate the
value ofx and ofy that satisfy the following
simultaneous linear equations:
545
22
yx
yx
[6 marks]
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7/31/2019 11. N
10/12
109
9 (a) Given that
23
1nP .
(i) Calculate the value ofn, if matrix P has no inverse.(ii) Ifn
= 5, find the inverse of matrix P.
(b) Hence, by using matrices, calculate the value ofx and ofy
that satisfy the
following matrix equation:
1
7
23
15
y
x
[6 marks]
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7/31/2019 11. N
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110
10 (a) It is given thatMis a 22 matrix such that
10
01
45
23M .
Find matrixM.(b) Write the following simultaneous linear
equations as matrix equation.
745
423
wu
wu
Hence, using matrices, calculate the value ofu and ofw.
[6 marks]
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7/31/2019 11. N
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111
