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(Topic 2

Matrices & Systems of Linear Equations)

Mathematics 2

MTH1022

ANSWER SCHEME

1. What is the order of each matrix.a. A = [1 ] b. B = c. C =

2. Given that the following matrices are equal, find the values ofx, y andz.

a. 3. Determine the values of [ ] .

4. Find the values of if 5. Given , find the value of and

[ ]

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6. Given , find the values of and . 7. Find the values if . 8. Given Find the values of and

9. Determine the values of and if[ ] . 10.Find the values

if

[ ] 11.Given that and , find :

a.

b.

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12.Given , and . Find :a.

b.

[ ]

13.13. Given , find :

a.

b.

||

14. Given , find :

a.

b. ||

15.If and , find :

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a. [ ]

b.

[ ]

16.Given Find :a.

[ ]

b. determinant of matrix ||

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17.Solve the following by using Cramers Rule:i. x + yz = -2

ii. 2xy + z = 5iii. -x + 2y + 2z = 1

||

18.Solve the following by using Cramers Rule:i. 3x4y + 4z = 7

ii. xy2z = 2iii. 2x + 3y + 6z = 5

||

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19.Solve the following systems of equations using Cramers Rule.i.

ii.

||

and

i. ii.

||

20.The table below gives the number of cakes sold by three classes to raise funds for theirschool .

Form

Plain

Cake

Marble

Cake

Carrot

Cake Total

2 p 2m 3c 19

4 2p 4m 5c 34

6 3p 5m 6c 42

Express this information in the form of a matrix equation , where is a squarematrix of order 3 and both and are column matrices with

( ) (

)Find ||.

||

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a. Find.