This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Assignment 4: Matrices Due: 29 nd October Name: __________________ 1. Given the matrix A =  2 1 3 find the values of the real number k for which det( A kI ) = 0 where I = 1 1 . Working: Answer: .............. (Total 4 marks) 2. (a)Find the values of a and b given that the matrix A =  4 7 6 3 5 4 5 8 a is the inverse of the matrix B = . 3 1 2 1 2 1 3 1  b (b) For the values of a and b found in part (a), solve the system of linear equations x + 2 y 2 z = 5 3 x + by + z = 0 x + y 3 z = a 1. Working: Answers : (a) .................................................................. (b) .................................................................. (Total 4 marks) 1 3. Find the values of the real number k for which the determinant of the matrix + 1 3 2 4 k k is equal to zero. Working: Answer: .................................................................. (Total 3 marks) 4 . (a)Given matrices A , B , C for which AB = C and det A 0, express B in terms of A and C . (2) (b) Let A =  2 2 3 3 1 2 3 2 1 , D =  5 4 7 9 7 13 3 2 4 and C = 10 7 5 . (i) Find the matrix DA ; (ii) Find B if AB = C . (3) (c) Find the coordinates of the point of intersection of the planes x + 2 y + 3 z = 5, 2 x y + 2z = 7 and 3 x 3 y + 2 z = 10. (2) (Total 7 marks) 2 5. If A = 2 4 4 x and B = 4 8 2 y , find 2 values of x and y , given that AB = BA . Working: Answer: .......................................................................... (Total 3 marks) 6. The matrix k k 5 3 13 1 3 2 1 is singular. Find the values of k . Working: Answer: .......................................................................... (Total 3 marks) 3 7. The matrix A is given by A = 2 4 3 1 1 1 2 k k Find the values of k for which A is singular. Working: Answer: .......................................................................... (Total 6 marks) 8. (a) Find the determinant of the matrix 5 1 2 1 2 1 2 1 1 (1) (b) Find the value of for which the following system of equations can be solved. = z y x 4 3 5 1 2 1 2 1 2 1 1 (3) (c) For this value of , find the general solution to the system of equations....
View Full
Document
 Spring '10
 wilson
 Math, Matrices

Click to edit the document details