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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 λ for which the following system of equations can be solved. = λ z y x 4 3 5 1 2 1 2 1 2 1 1 (3) (c) For this value of λ , find the general solution to the system of equations....
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 Spring '10
 wilson
 Math, Determinant, Matrices, ........., Invertible matrix, Kompakt, Kompakt albums, det M. Let M

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