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Form 3 Mathematics Matrices Questions and Answers
A and B are two Matrices.If
A
=
[
1
2
4
3
]
,find B given that
A
2
=A+B
(2m 1s)
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1.
Given that
A
=
[
2
4
3
6
]
and
B
=
[
11
3
4
1
]
find C such that B.C=A
2.
Find the inverse of the matrix
[
2
5
3
4
]
. Hence or otherwise solve the equation 2x+5y=9, 3x+4y=6
3.
Determine the value of X for which the matrix below has no inverse
[
2
x
x
2
2
1
]
4.
A clothes dealer sold 3 shirts and 2 trousers for sh.840 and 4 shirts and 5 trousers for sh.1680.Form a matrix equation to represent the above information .Hence find the cost of 1 shirt and the cost of 1 trouser.
5.
A and B are two Matrices.If
A
=
[
1
2
4
3
]
,find B given that
A
2
=A+B
6.
Given that A=
[
1
3
5
3
]
,B=
[
3
1
5
-
1
]
,C=
[
P
0
0
q
]
and AB=BC,determine the value of P
7.
A matrix A is given by A =
[
x
0
5
y
]
(a)Determine
A
2
(b)If
A
2
=
[
1
0
0
1
]
,Determine the possible pair of values of x and y.
8.
Given that p=
[
2
3
1
2
]
and Q=
[
2
-
3
-
1
2
]
find the matrix product PQ. Hence ,solve the simultaneous equation below: 2x-3y=5, -x+2y=-3
9.
Determine the inverse ,
T
-
1
of the matrix T=
[
1
2
1
-
1
]
Hence find the coordinates to the point at which the two lines x+2y=7 and x-y=1 intersect
10.
Given the simultaneous equations : 5x+y=19, -x+3y=9 (a)write the equations in matrix form .Hence solve the simultaneous equations (b)Find the distance of the point of intersection of a line 5x+y=19 and –x+3y=9 from the point (11,-2)
11.
(a)Find the inverse of the matrix
[
9
8
7
6
]
. (b) In certain week a businessman bought 36 bicycles and 32 radios for a total of ksh.227,280.In the following week ,he bought 28 bicycles and 24 radios for a total of ksh.174,960.Using matrix method ,find the price of each bicycle and each radio that he bought. (c) In the third week,the price of each bicycle was reduced by 10%
12.
Two matrices A and B are such that A=
[
k
4
3
2
]
and B=
[
1
2
3
4
]
Given that the determinant of AB=4,find the value of k
13.
Matrix P is given by
(
4
7
5
8
)
(a) Find
P
-
1
(b) Two institutions, Elimu and Somo, purchased beans at sh. b per bag and maize at sh. m per bag. Elimu purchased 8 bags of beans and 14 bags of maize for sh. 47,600. Somo purchased 10 bags of beans and 16 bags of maize for sh. 57,400. (i) Form a matrix equation to represent the information above.
14.
Given that
A
=
(
-
2
3
4
-
1
)
and
B
=
(
-
20
30
40
-
10
)
(i) Find
A
-
1
B
. (ii) Hence or otherwise write down the inverse of B
15.
(a) The product of matrices
[
0
1
2
p
]
and
[
-
1.5
-
0.5
p
p
-
2
]
is a singular matrix. Find the value of p (b) A sales woman earned a fixed salary of ksh x and a commission of ksh y for each item sold .In a certain month she sold 30 items and earned a total of ksh 50,000.The the following month she sold 40 items and earned a total of ksh 56,000. (i) Form two equations in x and y.
16.
Given that A=
[
1
0
-
2
3
]
,B=
[
3
0
2
1
]
and C=2AB-
A
2
.Determine matrix C
17.
A trader bought 2 cows and 9 goats for a total of Ksh.98,200.If she had bought 3 cows and 4 goats she would have spent ksh.2200 less. (a) Form two equations represent the above information (b) Use matrix method to determine the cost of a cow and that of a goat. (c) The trader later sold the animals she had bought making a profit of 30% per cow and 40% per goat (i)calculate the total amount of
18.
Two shopkeepers,Juma and Wanijku bought some items from a wholesaler.Juma bought 18 loaves of bread ,40 packets of milk and 5 bars of soap while Wanjiku bought 15 loaves of bread ,30 packets of milk and 6 bars of soap.The prices of a loaf of a bread , a packet of milk and a bar of soap were ksh 45,ksh 50 and ksh 150 respectively. (a) Represent: (i)the number of items bought by Juma and Wanjiku
19.
(a)Given that A=
[
3
x
x
+
1
2
]
and B=
[
1
2
3
0
]
,find the values of x for which AB is a singular matrix. (b) Mambo bought 3 exercise books and 5 pens for a total of ksh 165.If Mambo bought 2 exercise books and 4 pens ,he would have spent ksh 45 less .Taking x to represent the price of an exercise and y to represent the price of a pen. (i) Form two equations to represent the above
20.
Use the matrix method to solve 5x+3y=3 3x-4y=-8
21.
Give thatA=
[
2
3
4
4
]
,B=
[
x
1
2
3
]
and that AB is a singular matrix ,find the value of x
22.
(a) Find
A
-
1
,the inverse of matrix A=
[
5
6
7
9
]
. (b) Okello bought 5 physics books and 6 mathematics books for a total of ksh 2440.Ali bought 7 physics books and 9 mathematics books for a total of ksh 3560. (i)Form a matrix equation to represent the above information. (ii)use matrix method to find the price of a physics book and that of a mathematics book.
23.
Use matrices to solve the simultaneous equations: 4x+3y=18 5x-2y=11
24.
(a) Given that the matrix A =
(
2
3
3
4
)
, find
A
-
1
, the inverse of A. (b) Kantai bought 200 bags of sugar and 300 bags of rice for a total of sh. 850,000. Buya bought 90 bags of sugar and 120 bags of rice for a total of sh. 360,000. If the price of a bag of sugar is sh. x and that of rice is sh. y, (i) Form two equations to represent the information above.
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