NATION DAILY
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PURSUING JUSTICE AND EQUITY WITH INTEGRITY Vol. 6. Issue 2701
Price K10
Saturday September 5, 2020
HH ‘ADMITS’ FRAUD ALLEGATIONS By NATION REPORTER
U
PND president Hakainde Hichilema has “admitted” that he acted criminally in selling Intercontinental Hotel in Livingstone without declaring interest, by failing the accusation made by former Minister of Finance Editrh Nawakwi. After promising to sue her
for the allegation, Mr Hichilema has instead sued her for buying a house from Lima Bank. Mr Hichilema has “admitted” that he acted fraudelently and criminally by selling Intercontinetal Hotel to himself without declaring interest, an accusation made by Ms Nawakwi. To Page 3
Mr Hichilema
HH FAILS TO CHALLENGE NAWAKWI
Find strategic partner South chiefs in Mopani – Kavindele pledge to curb By SILUMESI MALUMO
GOVERNMENT must find a strategic partner to run Mopani Copper Mines (MCM) even if it wants to buy all the shares offered to it by Glen-
Mr Kavindele
core, former Vice President Enock Kavindele has said. Mr Kavindele said it will be very costly for the state to run the mining firm as the venture requires huge sums of money. To Page 3
UBZ properties worth $5.5bn To Page 3 vanish
tribalism
To Page 3
By SILUMESI MALUMO
CHIEFS from Southern Province have resolved to work with Government to end tribalism in the country. Traditional leaders include Chief Mukobela of Namwala, Chieftainess Sikute of Kazungula, Chief Hamaundu of Pemba and Chief Chikanta of Kalomo. Others are Chief Cooma of Choma, Chieftainess Mweenda of Chikankata, Chief Moonze and Chief Chikanta of Dundumwenzi. To Page 3
Mukula ban stays - Kapata
PURSUING JUSTICE AND EQUITY WITH INTEGRITY
Saturday 5 September, 2020
NORTH-WESTERN/ MOSI-OA-TUNYA NEWS
Nine shops shut in L/Stone By ANDREW MUKOMA
COPS NAB CONGOLESE, …recover TWO OTHERS explosives By JACKSON MAPAPAYI
P
OLICE in Solwezi have detained two men and a woman for unlawful possession of explosives. The three have been identified as Emmanuel Chitambala, 52, a Congolese,
Esther Mwansa, 40 of Roma Township in Lusaka and Emmanuel Mujimanzovu, 29 of Kaunda Square in Lusaka. North-Western Province Police Commissioner Elias Chushi who confirmed the incident explained that his officers intercepted a Toyota Hilux registration umber AAR
3517 which was being driven by Mujimanzovu. "And upon searching the vehicle, police found a carton box containing 156 innopak explosives, three electric detonators, one roll of white electrical cable, one small yellow cable and 23 non-detonators," he said.
Mr Chushi said after being interrogated, the suspects failed to give any convincing reasons as to how the explosives were in their possession. He said the suspects have since been remanded in police custody awaiting court appearance while the motor vehicle has been impounded.
THE Livingstone City Council (LCC) has closed nine shops that deal in hardware and assorted food items for failing to pay various levies. The shops were shut during the Revenue Task Team routine levy collection exercise, with some shop owners scampering ifor fear of being penalised. But some traders have complained of poor income as their reason for failing to pay, urging the local authority to allow them to reopen businesses. Traders complained that they had been affected by the effects of Covid-19. The operations was carried out at Livingstone’s Dambwa North Market Mr Eddie Tembo, who deals in hardware, said the council would find it difficult to collect levies if it continued “harassing” traders. Mr Tembo called on the
DAILY
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ward Councillor, Owen Muteba, to help address the situation at the market. He said in an interview that business had been slow since the outbreak of the Covid-19 in March this year. Dambwa North market committee vice-chairman, Samuel Limbali, was concerned that shops had been closed at the time traders were faced with challenges presented by Covid-19. Mr Limbali argued that the traders must be allowed to resume businesses adding that the local authority should come up with an affordable payment plan for traders to settle their dues. However, the council said it was prompted to close down the shops after owners failed to renew their licences within the two months’ grace period that was given in October 2019. Council Assistant Public Relations Manager Numba Mafwenko said for the council to continue giving services to the market traders should meet their financial obligations. Ms Mafwenko noted that the council was financially challenged and would not buy into COVID 19 excuses from the traders. She said that the council has since decided to add penalties for their failure to pay fire certificate and renewal of annual levies, among other statutory fees.
Cerebral palsy patient gets aid By ANDREW MUKOMA A 12-YEAR-OLD cerebral palsy patient in Livingstone has finally gotten help from a non-governmental organization following media reports about his condition. The boy's family has been shifted to a house which has running water and electricity, leaving the old house they occupied for many years in Linda compound. Philip Lubasi who has lived with the condition shortly after his birth in 2007 has challenges with his mobility and could not get to the washroom by himself. Philip's mother, Monica Lubasi, explained that her son was put on medication but his condition has remained the same. “My son was put on a lot of medication which did not help in any way. He had seizures which further affected his appetite and could not eat after being diagnosed with cerebral palsy," she explained. Ms Lubasi a single mother told the Daily Nation that her son has never spoken normally in addition to losing his sight. She added that she was only informed that Philip was
a cerebral palsy patient at the Livingstone Central Hospital after the prescribed medicine failed to work. “He cannot move even after many years of being on therapy at the Livingstone Central hospital. We have tried everything but nothing is working and the hospital informed us that he was also blind after failing to respond to simple exercises he was put on," she explained. The African Woman Foundation which supports over 6,000 vulnerable people across Africa, responded to Philip’s situation after a media report. The NGO donated a wheelchair and assorted food parcels, detergents, and mattresses. Foundation president, Joseph Moyo, said that it was a concern that Philip was subjected to an environment without water and electricity despite his condition which calls for proper care with running water. “Looking at the condition the boy is in, we decided to come in and help through our little resources by buying a few things such as food and mattresses and this wheelchair to aid his mobility.
“We also realised that hygienically the child was not well taken care of because he had mobility challenges which limited his movement to the toilet hence, we relocated the family to a house which has running water and electricity because they have to wash his clothes all the time," he said. Meanwhile, a community worker Alvin Mhongo has applauded the foundation for the gesture which included constructing a bay which would enable the wheelchair move in and out of the house without challenges. “We are very grateful that such an organization has come to the aid of this family with a cerebral palsy patient who had no access to clean water. “As a community worker, I urge the community to be vigilant on such issues involving marginalized people like Philip who needs proper care from all of us," he said. While the Foundation has committed to pay for the family's rentals for years to come, Philip's mother has also shown willingness to venture into a business to help support two of her daughters who are in school.
PUPILS Saturday 5 September, 2020
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Daily Nation, Educating Zambia!
SENIOR MATHEMATICS GRADE 10
SENIOR MATHEMATICS PREPARED BY: MR. BWALYA . K TOPIC: MATRICES
SUBTOPIC: INVERSE OF A 2 Ă— 2 MATRIX
INVERSE OF A đ?&#x;?đ?&#x;? Ă— đ?&#x;?đ?&#x;? MATRIX.
The inverse of a 2 Ă— 2 matrix is denoted by a letter to the power đ?‘Žđ?‘Ž đ?‘?đ?‘? ). Then its inverse is negative one. For example, if P is the matrix $ đ?‘?đ?‘? đ?‘‘đ?‘‘ +, denoted by đ?‘ƒđ?‘ƒ .
When finding the inverse of a 2 Ă— 2 matrix, the following steps must be followed:
(i) Find the determinant of the matrix. (ii) Find the co-matrix (iii) Multiply the co-matrix by the reciprocal of the determinant of the matrix. đ?‘Žđ?‘Ž đ?‘?đ?‘? đ?‘ƒđ?‘ƒ = $ ). đ?‘?đ?‘? đ?‘‘đ?‘‘
(i)
đ?‘‘đ?‘‘ −đ?‘?đ?‘? đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ @ ?đ??ˇđ??ˇđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ −đ?‘?đ?‘? đ?‘Žđ?‘Ž đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ
đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ??´đ??´=(5 Ă— 2) − (2 Ă— 1) = +,
đ??´đ??´
,
;<= >
đ?‘‘đ?‘‘ −đ?‘?đ?‘? $ ) −đ?‘?đ?‘? đ?‘Žđ?‘Ž
5 1 +, ) . đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??´đ??´ Example 1 2 2 K
2 −1 I = $ ) = J+K I −2 5 ,
I
10 − 21 = +, I L I
M=
8 ,
+,
N
I
N J+,
I L
2đ?‘Ľđ?‘Ľ + đ?‘Śđ?‘Ś = 5
7
2 1 ) 1 2 Find the determinant of the matrix shown. 2 1 ^ ^=3 1 2
8
$
4 1 ) 3 3
2. đ??şđ??şđ??şđ??şđ??şđ??şđ??şđ??şđ??şđ??ş đ?‘Ąđ?‘Ąâ„Žđ?‘Žđ?‘Žđ?‘Žđ?‘Ž đ?‘‡đ?‘‡ = $ value of x.
APPLICATION OF MATRICES.
Matrices can be used to solve system of equations by using: (a) Determinants (b) Inverse matrices. SOLVING SIMULTENOUES EQUATIONS USING DETERMINTS OF THE MATRIX.
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đ?‘Śđ?‘Ś =
đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘Śđ?‘Ś 3 = =1 đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘? đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š 3
đ?‘Ľđ?‘Ľ = 2
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Across
Down
1. Extravagant, wasteful 7. Very offensive 8. Paralyze with astonishment 9. Reinforced boot tip 10. Open a secure door 13. Eager, enthusiastic 15. Wonder how they live? (inf) 16. Early cave dweller
2. Oppose an argument 3. Taken flight 4. Fool 5. Severe (of an illness) 6. Overtook by a whole circuit 8. Unwise, without sense 11. Be more successful than others 12. Get ready to pray 13. Plant pest 14. Small island
đ?‘Śđ?‘Ś = 1
PUZZLE 30 SOLUTION W
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Simultaneous equations can also be solving by using the inverse matrix method.
A
3đ?‘Ľđ?‘Ľ − 2đ?‘Śđ?‘Ś = 10 (i)
(ii)
(iii)
đ?‘Ľđ?‘Ľ + 5đ?‘Śđ?‘Ś = −8
B
Write an the equation in matrix form. 3 −2 đ?‘Ľđ?‘Ľ 10 $ ) $đ?‘Śđ?‘Ś) = $ ) 1 5 −8 3 −2 ) Find the inverse of the matrix $ 1 5 5 2 − − 17@ đ?‘€đ?‘€ +, = ? 17 1 3 − 17 17 Multiply the inverse matrix on both sides of the matrix equation
$
đ??ťđ??ťđ??ťđ??ťđ??ťđ??ťđ??ťđ??ťđ??ťđ??ť đ?‘“đ?‘“đ?‘“đ?‘“đ?‘“đ?‘“đ?‘“đ?‘“ đ?‘‡đ?‘‡ +,
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SOLVING SYSTEM OF EQUATIONS USING INVERSE MATRIX METHOD.
2
3 2đ?‘Ľđ?‘Ľ ) and has determinant 3. Find the 2 7
đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘Ľđ?‘Ľ 6 = =2 đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘? đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š 3
(b) 5đ?‘Žđ?‘Ž + đ?‘?đ?‘? = 11 2đ?‘Žđ?‘Ž − 5đ?‘?đ?‘? = 26
TASK 1
1 2 5 3 ) đ?‘‹đ?‘‹ = $ ). 2 1 4 2
đ?‘Ľđ?‘Ľ =
(a) 3đ?‘Ľđ?‘Ľ − 2đ?‘Śđ?‘Ś = 8 đ?‘Ľđ?‘Ľ + đ?‘Śđ?‘Ś = 1
2 −2 1 −1 1 2 −2 4 4 2@ +, đ?‘ƒđ?‘ƒ = $ )=? @=? 2 −1 3 −1 3 4 −1 3 4 4 4 4
(iv) đ?‘Šđ?‘Šđ?‘Šđ?‘Š +, $
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TASK 2 4 Use the method of determinants to solve the following system of equations.
đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ?‘ƒđ?‘ƒ=(3 Ă— 2) − (1 Ă— 2) = 6 − 2 = 4
−1 5 −1 1 −5 đ?‘„đ?‘„+, = $ ) = ? 13 13@ 2 3 13 −2 −3 13 13
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Find the determinant of đ?‘Śđ?‘Ś(đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x; đ?‘Ąđ?‘Ąâ„Žđ?‘’đ?‘’ đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘? đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘Śđ?‘Ś đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤â„Ž đ?‘Ąđ?‘Ąâ„Žđ?‘’đ?‘’ đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) as 2 5 2 5 $ )=^ ^=3 1 4 1 4
M
đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ?‘„đ?‘„=(−3 Ă— 1) − (2 Ă— 5) = −3 − 10 = −13
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$5 1) 4 2 Find the determinant of X (đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x; đ?‘Ąđ?‘Ąâ„Žđ?‘’đ?‘’ đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘? đ?‘ đ?‘ đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘Ľđ?‘Ľ đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤â„Ž đ?‘Ąđ?‘Ąâ„Žđ?‘’đ?‘’ đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) 5 1 5 1 )=^ đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ?‘Ľđ?‘Ľ = $ ^=6 4 2 4 2
đ?‘ƒđ?‘ƒ +, đ?‘„đ?‘„+,
(i) đ?‘Šđ?‘Šđ?‘Šđ?‘Š (ii) đ?‘Šđ?‘Š +, (iii) đ?‘‹đ?‘‹ +,
3
Write down the matrix using the coefficients of the variables in the two equations.
Find
Find
2
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đ?‘Ľđ?‘Ľ + 2đ?‘Śđ?‘Ś = 4
Example 2.
1. Given that đ?‘Šđ?‘Š = $
1
Example solve the following system of equations.
3 2 −3 5 Given that đ?‘ƒđ?‘ƒ = $ ) đ?‘„đ?‘„ = $ ) 1 2 2 1 (i) (ii)
PUZZLE 31
THE CRAMMER’S RULE.
đ?‘Ľđ?‘Ľ + 2đ?‘Śđ?‘Ś = 4
(iii). The inverse of a 2 Ă— 2 matrix is given by đ?‘ƒđ?‘ƒ +, =
Given that đ??´đ??´ = $
TOPIC: MATRICES | GRADE: 10
2đ?‘Ľđ?‘Ľ + đ?‘Śđ?‘Ś = 5
đ??ˇđ??ˇđ??ˇđ??ˇđ??ˇđ??ˇ đ?‘ƒđ?‘ƒ = (đ?‘Žđ?‘Ž Ă— đ?‘‘đ?‘‘) − (đ?‘?đ?‘? Ă— đ?‘?đ?‘?) = đ?‘Žđ?‘Žđ?‘Žđ?‘Ž − đ?‘?đ?‘?đ?‘?đ?‘? đ?‘‘đ?‘‘ −đ?‘?đ?‘? đ??śđ??śđ??śđ??ś − đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š $ ). −đ?‘?đ?‘? đ?‘Žđ?‘Ž
(ii)
PREPARED BY: MR. BWALYA . K
1 0
5 2 5 − − 17@ $3 −2) $đ?‘Ľđ?‘Ľ ) = ? 17 ? 17 đ?‘Śđ?‘Ś 1 3 1 1 5 − − 17 17 17 5 2 0 đ?‘Ľđ?‘Ľ 17@ $ 10 ) ) $ ) = ? 17 1 3 1 đ?‘Śđ?‘Ś −8 − 17 17
34 5 2 Ă— 10 + Ă— (−8) đ?‘Ľđ?‘Ľ 2 17 17 5 @ = $ ) $đ?‘Śđ?‘Ś) = ? 17 @ = ? 34 5 23 −34 −1 −2 Ă— (−8) đ?‘Ľđ?‘Ľ Ă— 10 10 + + 17 Ă— Ă— (−8) 2 17 17 17 $đ?‘Śđ?‘Ś) = ? 17 @ = ? 17 @ = $ ) −34 3 −1 −2 Ă— 10 + Ă— (−8) 17 17 17 đ?‘Ľđ?‘Ľ 2 $đ?‘Śđ?‘Ś) = $ ) −2 đ?‘Ľđ?‘Ľ 2 $đ?‘Śđ?‘Ś) = $ ) −2 đ?‘Ľđ?‘Ľ = 2 đ?‘Śđ?‘Ś = −2 đ?‘Ľđ?‘Ľ = 2 đ?‘Śđ?‘Ś = −2
2 17@ $ 10 ) 3 −8 17
TASK 3 Solve the following simultaneous equations using the inverse matrix method, TASK 3 (a) 3đ?‘Ľđ?‘Ľ − 2đ?‘Śđ?‘Ś = 5 Solve the following simultaneous equations using the inverse matrix method, đ?‘Ľđ?‘Ľ − đ?‘Śđ?‘Ś = 2 (a) 3đ?‘Ľđ?‘Ľ − 2đ?‘Śđ?‘Ś = 5 (b) 5đ?‘Ąđ?‘Ą + 3đ?‘&#x;đ?‘&#x; = 4 đ?‘Ľđ?‘Ľ − đ?‘Śđ?‘Ś = 2 4đ?‘Ąđ?‘Ą + đ?‘&#x;đ?‘&#x; = 6 (b) 5đ?‘Ąđ?‘Ą + 3đ?‘&#x;đ?‘&#x; = 4 4đ?‘Ąđ?‘Ą + đ?‘&#x;đ?‘&#x; = 6
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