Matrixes.docx

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Mathematics Matrixes 2012

1. .

Find , the inverse of the matrix . [2]

2.

(a) Find AB . [2]

(b) When , find the value of . [3]

3. The answer to this matrix multiplication is of order .Find the values of and . [2]




4. Work out .

[3]

5.

(a) The matrix .Calculate B.Show all your working. [4]

(b) Simplify . [1]

6. .

(a) Find , the determinant of A, in terms of . [1]

(b) Find the values of when . [2]




7. (a) Find . [2]

(b) .

Find the values of and . [2]

(c) Explain why does not have an inverse. [1]

8. Calculate . [2]




9. .

Calculate the value of , where and are the determinants of and .[2]

10.

.

Find(a) , [1]

(b) . [2]

11. .

(a) Write as a single matrix(i) , [2]

(ii) . [2]




(b) Find . [2]

12.

(a) Which one of the following matrix calculations is not possible (i) ,(ii) ,(iii) ,

(iv) .[2]

(b) Calculate . [2]

(c) Use your answer to part (b) to write down , the inverse of . [1]

13. (a) Multiply . [2]

(b) Find the inverse of . [2]




14. .

(a) Find the matrix , such that . [2]

(b) Find the matrix , such that . [3]

15.

.

(a) .(i) Write down an equation in . [1]

(ii) Find the value of . [1]

(b) Explain why does not have an inverse. [1]

(c) Find , the inverse of . [2]




16. Given the matrices and , work out

(a) , [2]

(b) , the inverse of . [2]

17. , , ( ).(a) If , find the value of and the value of . [3]

(b) Find , the inverse of . [2]




18. Given that matrix .

(a) Calculate the value of the determinant of , [1]

(b) Write down . [1]

19. Given that and .

(a) Find(i) , [1]

(ii) the inverse of matrix . [2]

(b) Write down

. [1]




20. The matrix .

(a) Write down an expression, in terms of , for the determinant of . [1]

(b) Given that the determinant of is ,(i) Calculate the value of , [1](ii) Write down . [1]

21. The matrix .

Given that the determinant of is .(a) Find

(i) the value of , [2]

(ii) . [1]




(b) Write down . [1]

22. It is given that

.

Find(a) , [2]

(b) . [2]




23. .

Find(a) , [2]

(b) , [2]

(c) . [2]

24. (a) The matrix satisfies the equation .

Find , expressing it in the form

. [2]

(b) Find the inverse of the matrix . [2]




25. (a) The determinant of the matrix is .

Find . [2]

(b) Find the inverse of the matrix . [2]

26. and .

Find(a) , [2]

(b) . [2]




27. , , , .

Find

(a) , [1]

(b) , [2]

(c) , [1]

(d) . [2]




28. Given that and .

Find(a) , [2]

(b) the determinant of , [1]

(c) . [1]

29.

(a) Calculate(i) , [1]

(ii) , [2]

(iii) . [2]

(b) Explain why does not have an inverse. [1]




30. (a) ,

Find(i) ,

(ii) ,

(iii) the determinant of ,

(iv) .

[5]

(b) (i) Multiply out the matrices on the left hand side and hence write down threeequations.

[3](ii) , and all represent positive integers.

By solving your equations, or otherwise, find the value of of and of . [4]

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Matrixes.docx