a) Write down the 3 x 3 matrices A, B and C with entries aij =...

  

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a) Write down the 3 x 3 matrices A, B and C with entries aij = i, bij = i/j and cij = i, respectively. Compute AB, BA and C2. b) [2 marks] Find det(C). c) [2 marks] If det(M) = 2 and det(N) i det (NM-N). ii det (MON (M-1)4(N-1)³). = 3, calculate: d) [2 marks] Use the Gauss-Jordan algorithm to find the inverse of the following matrix 1 0 0 0 4 4 4 01 e) [3 marks] For the following system of equations write down the augmented matrix, find its reduced row echelon form and then use it to write down the solutions to the system x + 4y +4z x + 8y +8z 5х + 4y + 52 1 1 -2. f) [3 marks] For the following system of equations write down the augmented matrix, find its reduced row echelon form and then use it to write down the solutions to the system 1 x1 - x3 4.x1 – 2x4 -2 2х2 — 2х3 — 24 1. I| |||| a) Write down the 3 x 3 matrices A, B and C with entries aij = i, bij = i/j and cij = i, respectively. Compute AB, BA and C2. b) [2 marks] Find det(C). c) [2 marks] If det(M) = 2 and det(N) i det (NM-N). ii det (MON (M-1)4(N-1)³). = 3, calculate: d) [2 marks] Use the Gauss-Jordan algorithm to find the inverse of the following matrix 1 0 0 0 4 4 4 01 e) [3 marks] For the following system of equations write down the augmented matrix, find its reduced row echelon form and then use it to write down the solutions to the system x + 4y +4z x + 8y +8z 5х + 4y + 52 1 1 -2. f) [3 marks] For the following system of equations write down the augmented matrix, find its reduced row echelon form and then use it to write down the solutions to the system 1 x1 - x3 4.x1 – 2x4 -2 2х2 — 2х3 — 24 1. I| ||||

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