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Form 3 Mathematics Matrices Questions and Answers
Use matrices to solve the simultaneous equations:
4x+3y=18
5x-2y=11
(3m 16s)
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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 #[[2x, 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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